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Application surjective 1999-09-30
Charass pose la question :
je suis étudiant en premiere année de deug et je cherche apres une definition si vous pouviez m'aider, ça serait sympa. qu'est ce qu une application subjective?
Claude Tardif lui répond.
Input and output of a function 2019-12-16
Destanie pose la question :
What is the output if the input is -1???
Penny Nom lui répond.
A function problem 2019-12-12
akash pose la question :
if (2,1) is on the f(x), what is the coordinate of the corresponding point of -2(f(2x-6)+5?
Penny Nom lui répond.
Algebra 2019-11-06
Krizhia pose la question :
How is y= 1/2 * (x-1)² be x= √2y + 1. Please show me the steps
Penny Nom lui répond.
f(x + 2) 2019-02-26
a student pose la question :
How do you use f(x) = 3x+1 to determine the transformed function of f(x + 2)?
Penny Nom lui répond.
Composition of functions 2019-02-24
Joshua pose la question :
Let g(x)=(x)^(2)+x-1 Find such a function f such that (fog)(x)=(x)^(4)+2(x)^(3)-3(x)^(2)-4x+6
p lui répond.
Function notation 2019-02-10
Paige pose la question :
What is the difference between f(x+2) and f(x)+2?
Penny Nom lui répond.
y=lnx+(1+ln2)/2 and y=x^2 2019-01-28
Mike pose la question :
Prove that y=lnx+(1+ln2)/2 and y=x^2 touch each other.

The course is about logarithm and root functions... how should I solve this problem?

Penny Nom lui répond.
y = f(x) 2018-12-30
yogita pose la question :
What is the actual meaning of "f(x)" ? Please give me full explanation
Penny Nom lui répond.
y = |x| - 1 2018-11-30
alexis pose la question :
what does this mean y=|x|-1
Penny Nom lui répond.
f(x) and f(-x) 2018-10-19
Simran pose la question :
what is difference between f(x) compared to f(-x) on graph
Penny Nom lui répond.
The domain of f(g(x)) 2018-06-18
Joshua pose la question :
What are the restrictions of the domain of f(g(x))?
Penny Nom lui répond.
Positive and negative values of a function 2018-01-30
Grayson pose la question :
f(x)=x^6-x^4
Interval: ( negative infinity, negative one )
Test Value: negative two
Function Value f(x): positive forty eight
Interval: ( negative one, zero )
Test Value: negative one
Function Value f(x): zero
Interval: ( zero, positive one )
Test Value: positive one
Function Value f(x): zero
Interval: ( positive one, positive infinity )
Test Value: positive two
Function Value f(x): positive forty eight

What is the sign of f(x) for each Interval?

Penny Nom lui répond.
f(x)=-x^2-6x find f(x-2) 2017-10-27
Kenneth pose la question :
f(x)=-x^2-6x find f(x-2)
Penny Nom lui répond.
y = g(x + 1) 2017-06-27
Shamsudiin pose la question :
HI there i am currently doing a level maths AS

I don't understand how to graph this Question y=g(x+1) i really need help please please respond to this problem

Penny Nom lui répond.
A function which is onto but not one-to-one 2017-04-16
Avinash pose la question :
Define a function f(x):N-->N which is onto but not one-one.Where N is set of natural numbers.
Penny Nom lui répond.
The inverse of y=x^2+x+c 2016-12-21
Sam pose la question :
What is the inverse of y=x^2+x+c for x?
Penny Nom lui répond.
The inverse of y = x(x - 2) 2016-12-21
Sasha pose la question :
Hello, I recently stumbled upon this question and I haven't been able to figure it out.

Why is the inverse of y=x(x-2) not a function?

Suggest a domain restriction which would ensure that the inverse is a function.

Thank You :)

Penny Nom lui répond.
The derivative of the inverse of a function 2016-10-28
Kate pose la question :
Hi, I'm in a College level Calculus course and I can't seem to figure out the answer to this question.
Find the derivative of f^-1(4) if f(3)=4 and f'(3)=1/7

Penny Nom lui répond.
A linear relationship 2016-10-16
Bianca pose la question :
x represents the number of hours since 8am. y represents the number of children the school nurse has seen during the school day. The nurse has seen 3 children by 8am and 27 children by noon.
How many children has the nurse seen at 2pm?
If the nurse has seen 18 children, what time is it?

Penny Nom lui répond.
The temperature inside and outside a greenhouse 2016-07-22
Mehzad pose la question :
Every day, the temperature in a greenhouse is at its low temperature, 70 degrees Fahrenheit, at 2 a.m. and at its high temperature, 84 degrees Fahrenheit, at 2pm. Its temperature increases linearly between 2 am and 2pm , and decreases linearly from 2 pm and to 2am. The outside temperature follows the same linear patterns, but has a low temperature of 60 degrees Fahrenheit at 2 am and a high temperature of 78 degrees Fahrenheit at 2 pm. At which of the following times will the temperature inside and outside the greenhouse be the same?

a) 8:00 am
b) 12:00 noon
c) 4:00 pm
d) The two temperatures will never be the same

Penny Nom lui répond.
The composition of a function with itself 2016-07-17
Mel pose la question :
If f(1 + 3x) = 1 * x, solve f(f(x))
Penny Nom lui répond.
find f+g 2016-06-26
yzabelle pose la question :
find f+g
f(x)=x^2-1
g(x)=square root of x+2

Penny Nom lui répond.
sin 2x - sin x = 0 2016-04-24
lilly pose la question :
sin 2x - sin x = 0 0
Penny Nom lui répond.
The inverse function for f(x)=2x^2+5x 2016-04-23
Ashini pose la question :
The inverse function for f(x)=2x^2+5x
Penny Nom lui répond.
The inverse of a function 2016-03-20
Billy pose la question :
f(x) = Square root(x^2 + 2x)

What is the inverse?

Penny Nom lui répond.
The domain and range of a function 2016-02-19
Genius pose la question :
State the domain and range g(x)=x(x-1)
Penny Nom lui répond.
The range of a function with a finite domain 2016-01-25
Hannah pose la question :
Solve y=(1⁄4)x-1 if the domain is (-4,-2,0,2,4). I don't get how to do this. Can anyone help?
Penny Nom lui répond.
A limit of a rational function 2016-01-16
selvamani pose la question :
F (x) = x^3+3x^2-9x-2 / x^3-x-6 and limit x tends to 2, f (x) exist then limit x tends to 2, f (x) is equal to ? How to answer this problem.
Penny Nom lui répond.
The range of a function defined piecewise 2016-01-13
sarah pose la question :

f(x)={x-2, x<-2
       {x^2-4, -2_<x_<2
       {x+2, x>2

find the range
Penny Nom lui répond.

The range of f(x)=(2x+2)/(x-1) 2015-11-25
Nazrul pose la question :
f : R to R is a function which is defined by f(x)=(2x+2)/(x-1).
Is f(x) an onto function? Please explain.
What is the range of this function?
Thank you very much for your previous help.

Harley Weston lui répond.
Fencing around a rectangular field 2015-11-11
Darlene pose la question :
Question from Darlene, a parent: A farmer has 10,000 meters of fencing to use to create a rectangular field. He plans on using some of the fencing to divide the rectangular field into two plots of land by constructing a fence inside the rectangle that is parallel to one of the sides. Let X be the width of the rectangular field. Write an equation to express the area of the field as a function of X. Find the value of X that maximizes the area of the field.
Penny Nom lui répond.
The domain of cos2x/(sinx-2) 2015-11-02
Ameen pose la question :
Find the domain of:
f(x) = cos2x/(sinx-2)

Penny Nom lui répond.
y=f(x) and y=-3/2f(x) 2015-05-27
Kevin pose la question :
Could you please show me what change y=f(x) to y=-3/2f(x) has gone through and please graph.

y=f(x) points: (-3,0) ,(0,-2), (2,-2), (3,4)

how does (0,-2) change?

Penny Nom lui répond.
A piecewise function 2015-04-25
uday pose la question :

f(x)={x^2+3x+2 / x+2, x(not equal to)=-1
{4, x=-1
how to find domain and how the graph looks like


Penny Nom lui répond.
Solve x=r(t-sin(t)) for t 2015-02-28
David pose la question :
I don't know how to write the function of t(x) by x=r(t-sin(t)).
Can you teach me that?

Harley Weston lui répond.
A stone is dropped in a lake 2015-02-14
Wendy pose la question :

Hi, I have problems solving this problem. We didn't exactly go over these kind of problems and the book doesn't have an example either. Thank you for your help!

A stone is dropped in a lake, creating a circular ripple that travels outward at a speed of 80 cm/s.
(a) Find a function g that models the radius as a function of time t.

g(t) =

(b) Find a function f that models the area of the circle as a function of the radius r.

f(r) =

(c) Find f compose g.
f compose g =


Penny Nom lui répond.
Continuity on a closed interval 2014-09-21
Pragya pose la question :
The trouble I'm having is as follows :
a continuous function is most of the times defined on a closed interval, but how is it possible to define it on a closed interval ,because to be continuous at endpoints of the interval the function's limit must exist at that endpoint,for which it has to be defined in its neighborhood,but we don't know anything about whether the function is always defined in the neighborhood.
Please help...

Penny Nom lui répond.
What is this function? 2014-04-17
Keta pose la question :
What is this function?
-12=-2
-6=-1
6=1
0=0

Penny Nom lui répond.
The locus of a point 2014-04-04
srishti pose la question :
A point P moves such that the difference between its distance from the origin and from the axis of x is always a constant c . what is the locus of the point?
Penny Nom lui répond.
Graphing piecewise functions 2014-03-29
Rayven pose la question :
Hi! I'm in eighth grade, taking ninth grade algebra 1. I'm confused as to how to graph piecewise functions. I know that you have already answered a question similar to this (I did my research first) but it didn't completely help me on my homework. I have to graph piecewise functions for the specified domains, and create a table for the absolute values. I know that two bars around a number means absolute value (two bars around -2 makes it +2) , but how do I graph and chart the absolute value for the following:

f(x)= |x+3 | for -5≤x≤3

And then graph and chart: (on a separate graph):

f(x)= {x if x≤0
{x+1 if x <0

thank you!
~Rayven

Penny Nom lui répond.
A limit with trig functions 2014-02-22
pearl pose la question :
(what is the value of limit of x as it approaches 0 of sin8x divided by cos6x)
Penny Nom lui répond.
Water in a conical funnel 2014-02-11
Marcus pose la question :
Water is running out of a conical funnel at the rate of 1 inch^3/sec. If the radius of the base of the funnel is 4 in. and the altitude is 8 in., find the rate at which the water level is dropping when it is 2 in. from the top.
Penny Nom lui répond.
What does y= f(x) actually mean? 2013-12-31
John pose la question :

I don't understand how to pick coordinates for y=f(x).

I took a look at your answer to a previous question here:

http://mathcentral.uregina.ca/QQ/database/QQ.09.00/monica2.html

What does y= f(x) actually mean?


Penny Nom lui répond.
Inverse trig functions 2013-05-19
ky pose la question :
hello, so iv'e been asked to draw a triangle with sides of 3, 4, and 5. And find the measure of all three angle using sin-1, cos-1, tan-1. I got really confuse, I'm taking the SAT pretty soon and it would be great to get this... THANX
Penny Nom lui répond.
How do i write log_8(P) =7 in exponential form? 2013-04-14
nancy pose la question :
How do i write this in exponential form log8P =7
Penny Nom lui répond.
The continuity of f(x,y)=ln(x^2+y^2) 2013-02-17
anu pose la question :
the question says we have to find the points in the plane where the function is continuous: f(x,y)=ln(x^2+y^2) . here we aren't given a particular point (x,y) where we have to check a function's continuity. what is to be done if we have to check continuity over the whole domain of the function? please help .
Harley Weston lui répond.
What is the domain of f(x)=sin(ln(x))/ln(x)? 2013-02-06
Behrooz pose la question :
Hi, the following problem may be interesting: What is the domain of f(x)=sin(ln(x))/ln(x)? Be careful, domain is not obvious. Best regards Behrooz
Penny Nom lui répond.
An area bounded by lines 2012-12-16
sidra pose la question :
find area bounded by functions:
y=x
y=2x
and y=5-x

Penny Nom lui répond.
A function problem 2012-11-18
nahla pose la question :
f: IN --> IN
n --> f(n)
for every n that belongs the IN : fof(x) = 4n - 3
and for every n that belongs to IN f(2^n) = 2^(n+1) -1

Calculate f(993)

Penny Nom lui répond.
The derivative of y = sin (30º + x) 2012-11-07
Saskia pose la question :
derivative of y = sin (30º + x)
Harley Weston lui répond.
Introductory algebra 2012-10-30
kevon pose la question :
if x = 7 is used in the expression 2x + 5 what is the output
Penny Nom lui répond.
A function with 3 asymptotes 2012-10-19
rimoshika pose la question :
find a function that have 3 Asymptotic : y=x/y=sinx/x=-1
Penny Nom lui répond.
Composition of functions and one to one 2012-10-17
Ariana pose la question :
If f o g are one to one function,does it follow that g is one to one? Give reasons for your answers
Penny Nom lui répond.
Functions 2012-09-18
nayeem pose la question :
I tried with many functions but I am not getting the exact values please help me
A give an example of a function whose domain equals the set of real numbers and whose range equals the set the set {-1,0,1}?
B Give an example of a function whose domain equals (0,1)and whose range equals [0,1] C.Give n example of a function whose is the set of positive integers and whose range is the set of positive even integers D. Give an example of a function whose domain is the set of positive even integers and whose range is the set of positive odd integers E give an example of function whose domain is the set of integers and whose range is the set of positive integers. F. Give an example of function whose domain is the set of positive integers and whose range is the set of integers.
please show me the work
Please give me the trick of finding such functions

Robert Dawson and Harley Weston lui répond.
Functions 2012-09-18
nayeem pose la question :
I tried with many functions but I am not getting the exact values please help me A give an example of a function whose domain equals the set of real numbers and whose range equals the set the set {-1,0,1}?
B Give an example of a function whose domain equals (0,1)and whose range equals [0,1] C.Give n example of a function whose is the set of positive integers and whose range is the set of positive even integers D. Give an example of a function whose domain is the set of positive even integers and whose range is the set of positive odd integers E give an example of function whose domain is the set of integers and whose range is the set of positive integers. F. Give an example of function whose domain is the set of positive integers and whose range is the set of integers.
please show me the work
Please give me the trick of finding such functions

Robert Dawson and Harley Weston lui répond.
The exponential function form f(x)=a^x 2012-08-13
Lucy pose la question :
Hi,
Why does the "a" value in the exponential function form f(x)=a^x have to be negative?

Penny Nom lui répond.
The range of h(x) = 1/x 2012-08-11
Lucy pose la question :
What is the range of the function: h(x)=1/x (and can you please explain why)?
Penny Nom lui répond.
A function from {a,b} to {p,q} 2012-08-10
Lucy pose la question :
How can a function relate each element of a set with exactly one element of possibly the same set?
Penny Nom lui répond.
The inverse of y = x^2 - 2x 2012-04-20
Shona pose la question :
How do I Find the inverse of the function y= x^2 - 2x ?
Penny Nom lui répond.
A uniform probability density function 2012-03-26
Noeline pose la question :
The label on a bottle of liquid detergent shows contents to be 12 ounces per bottle. The production operation fills the bottle uniformly according to the following probability density function:
f(x) = 8 for 11.975 ≤ x ≤12.10
and
f(x) = 0 elsewhere

a. What is the probability that a bottle will be filled with 12.02 or more ounces?
b. What is the probability that a bottle will be filled between 12 and 12.05 ounces?
c. Quality control accepts production that is within .002 ounces of number of ounces shown on the container label. What is the probability that a bottle of this liquid detergent will fail to meet the quality control standard?

Penny Nom lui répond.
The graph of a quadratic function 2011-12-27
Thomas pose la question :
sketch a quadratic function with zeros at -3 and 1
Penny Nom lui répond.
2 + f(x) and f(x) + 2 2011-11-21
Beth pose la question :
Do you do y=2+f(x) the same way as if the 2 came after the equation such as y=f(x) +2 when graphing?
Penny Nom lui répond.
Composition of functions 2011-09-05
Jenna pose la question :
Let f(x)=x^2-1 and g(x)=1-2x. Find the indicated values.
1. f(g(1)) and g(f(1))

Thanks,
Jenna

Penny Nom lui répond.
A step function 2011-08-22
Giovanna pose la question :
An average school bus holds 45 people. Show a graph between the relationship of students who need bus transportation and number of buses required?
Robert Dawson and Penny Nom lui répond.
The domain of a function 2011-05-08
Minks pose la question :
(x^2 + 1 / x^2 +2x - 3 ) X ( x^2 -9 / x^2 - 2x - 3)
Penny Nom lui répond.
tanθ=1.192 2011-01-15
Adori pose la question :
Use a calculator to approximate two values of the θ (0 ≤θ≤2π) that satisfy the equation. a) tanθ=1.192

I do not understand how to find the second value of θ.

Harley Weston lui répond.
Can a function be both even and one to one? 2010-10-09
Tracy pose la question :
Can a function be both even and one to one?
Harley Weston lui répond.
A pattern 2010-09-01
Hien pose la question :
How to find the pattern in this function?
x=1, y=o
x=2, y=1
x=3, y=1
x=4, y=2
x=5, y=2
x=6, y=3
x=7, y=3 and so on...

Tyler Wood lui répond.
An input-output table 2010-06-07
Brian pose la question :
Make an Input -output table to represent the function. Use 0,1,2,3 as the Domain. f(x)= 3+7x
Harley Weston lui répond.
graph y=(2x^2-3x)e^ax 2010-05-31
James pose la question :
graph y=(2x^2-3x)e^ax
Robert Dawson lui répond.
f(x) = x + 3 2010-05-02
becca pose la question :
Find the function value F(1)if f(x)=x+3
Penny Nom lui répond.
The intervals where the function is positive and negative 2010-01-10
Ron pose la question :
Hello

I'm trying to find out the intervals where the function is positive and negative. It's for a polynomial function y= -(x+2)^2 (x-2) and y= (x+1)(x+4)(x-3)

I have tried the right and left side of each x-intercepts, but I still don't understand the results

thank you for your help

Penny Nom lui répond.
Write a function for the area in terms of x 2010-01-01
Almarie pose la question :
Lauren has 40 feet of metal fencing material to fence three sides of a rectangular garden. A tall wooden fence serves as her fourth side. Write a function for the area of the garden A in terms of x, the width in feet.
Penny Nom lui répond.
Maximizing the area of a rectangle 2009-12-17
rachel pose la question :
A rectangular field is to be enclosed by 400m of fence. What dimensions will give a maximum area?
Penny Nom lui répond.
The inverse of f(x)=-1/x^2 2009-10-22
Jasmine pose la question :
how to solve f(x)=-1/x^2 --> find f-1[x], than state if its a function
Harley Weston lui répond.
y=2x+1 and y=2x-1 2009-08-28
MARICELA pose la question :
Need help of how to work this problems

y=2x+1 and y=2x-1

First of all what is the difference?

Second I think is easy just to work with the X y with the line in the middle

but how do you get the numbers for each side.

Penny Nom lui répond.
Graph 2x-3y+15=0 2009-08-20
Diem pose la question :
Graph 2x-3y+15=0
Leeanne Boehm lui répond.
An antiderivative problem 2009-08-13
Indrajit pose la question :
∫4e^x + 6e^-x/(9e^x + 4e^-x)dx = Ax + Bloge(9e2x - 4) + C

then A=?......B=?.....C=?

plz solve it...."^" stands for "to the power of"....

Harley Weston lui répond.
Area under curve 2009-07-21
Morag pose la question :
What is the area bounded by the curve y=X^2(2-X) and the x axis between x=0 and x=2?
Janice Cotcher lui répond.
The integral of a to power x squared 2009-04-28
JIM pose la question :
WHEN I ATTENDED U.OF T. (TORONTO ) MANY YEARS AGO WE WERE TOLD THE FOLLOWING INTEGRAL COULD NOT BE SOLVED : a to power x squared . is this still true ?

CURIOUS , JIM

Robert Dawson lui répond.
The integral of the square root of the sine function 2009-04-07
Indrajit pose la question :
how to integrate this derivative???

∫√sinx

Harley Weston lui répond.
An equation for a line with a changing slope 2009-03-21
Ben pose la question :
Is there anyway to write an equation for a line with a changing slope. e.g. A cell [hone company has a initial fee of 50$ paying for the first 100 minutes, the rate then increases to 10 cents per minute, then at 500 minutes the rate is 5 cents per minute.

If so please tell how.
Thanks

Penny Nom lui répond.
Trig functions without geometric data 2009-02-24
bob pose la question :
I do not understand how it is possible to find the sine, cosine, or tangent of an angle if there is no hypotenuse, opposite or adjacent side?!
Robert Dawson lui répond.
Intercepts in a Quadratic Function 2009-02-22
Barb pose la question :
I have a question I need help with please. What are the number of x and y intercepts that quadratic function can have and why? Thanks.
Janice Cotcher lui répond.
A piecewise function for monthly salary 2009-02-03
Josh pose la question :
A sales rep for a drug company is paid on the following scale. His base salary is $1600 per month. He is also paid a commission of 2% of sales over $20,000. When his gross sales reach $30,000 he is then paid 4% on the amount above that until his sales reach $50,000 after which point his commission becomes 6%. His commission reaches 8% when his sales total goes over $100,000 for the month. Set up a piecewise function for the information above.
Harley Weston lui répond.
The vertical line test 2009-01-26
bob pose la question :
what is a Vertical line test
Stephen La Rocque lui répond.
What is f^-1(3) when f(x)=2x-1? 2009-01-03
Peter pose la question :
how do you do functions like f^-1(3) when f(x)=2x-1?
Penny Nom lui répond.
A periodic function 2008-11-26
Ali pose la question :
A periodic function f(x) has a period of 9, if(2)=-3 and f(5)=13, determine the value of f(11)?

tks /rgrds

Ali

Penny Nom lui répond.
A conical funnel 2008-11-12
Rachael pose la question :
Hello, I am a 10th grader in AP Calc, and can not figure out this question: Water is running out of a conical funnel at the rate of 1 inch^3/sec. If the radius of the base of the funnel is 4 in. and the altitude is 8 in., find the rate at which the water level is dropping when it is 2 in. from the top.
Harley Weston lui répond.
Is it possible to a function to be both even and odd ? 2008-09-28
Mohammed pose la question :
Is it possible to a function to be both ( Even and Odd )
Harley Weston lui répond.
What is the derivative of (2^sinx)/(logbase4(2x+1))? 2008-09-16
Jesse pose la question :
What is the derivative of (2^sinx)/(logbase4(2x+1))
Harley Weston lui répond.
Limit as it Approaches a Constant 2008-09-16
Brooks pose la question :
what is the limit as x approaches 10 for f(x) = sqrt(x-1) = 3 pleeeeeaase help me out here
Janice Cotcher lui répond.
Function or Not? 2008-08-22
Katie pose la question :
Determine whether y is a function of x: [(x^2)y]-(x^2)+(4y)=0 ....thx
Janice Cotcher lui répond.
Graphing a piecewise function 2008-08-12
Shanti pose la question :
how do you graph a step function or piecewise function such as
u^2 if u is greater than or equal to -2 and less than 1
2- u if u is greater than or equal to 1 and less than 4

Penny Nom lui répond.
A linear function 2008-08-07
Warren pose la question :
What are the conditions of the numerical coefficients of the standard form Ax+By=C in Linear Function? How will you transform y=square root of 3 x + 1 in standard form Ax+By=C?
Penny Nom lui répond.
The product of the digits of a four digit number 2008-07-26
Pete pose la question :
I am a student preparing for a competition and this was one of the prep problems: The product of the digits of a four digit number is 6x5x4x3x2x1. how many such numbers are there with this property?
Stephen La Rocque lui répond.
Express as a function of x 2008-07-14
Rita pose la question :
Express the area A of an isosceles right triangle as a function of x of one of the two equal sides.

NOTE: I always see the phrase "Express as a function of x" in math textbooks.
What exactly does that phrase mean?
I also have seen it written as "Express in terms of x."

Penny Nom lui répond.
Composition of two functions 2008-07-04
Kristian pose la question :
f(x)= the square of x add to 1 and g(x)=1/x

find: (f o g)x

Penny Nom lui répond.
g(m-1,2n)+n 2008-06-07
Florence pose la question :
What does g(m-1,2n)+n for m>0, n>=0 mean.
Penny Nom lui répond.
The number of hours of daylight 2008-06-03
Marilyn pose la question :
Hi, could you please help me with this question? In a city (in the Northern Hemisphere) the minimum number of hours of daylight is 9.6 and the maximum number is 14.4. If the 80th day of the year (March 21) has 12 hours of daylight, determine a sine function which gives the number of hours of daylight for any given day of the year. (Jan 1 = 1, Jan 2 = 2, etc). Thank you!
Harley Weston lui répond.
The inverse of a function 2008-05-03
keith pose la question :
please help me find the inverse of this function:

h(t) = 2 + 4 ln(1-5t)

Stephen La Rocque lui répond.
Adding rational functions 2008-04-29
Jonathon pose la question :
1/(x+3) + 1/(x^2+5x+6) =
Penny Nom lui répond.
Two function problems 2008-04-10
keith pose la question :
find the domain: F(x)= 1/ {ln (x+5) - ln (7-x)}

find the inverse: g(t)= sqrt {2-3 ln (1-t)}

Penny Nom lui répond.
cosec [arccos (1/y)] 2008-04-09
Tom pose la question :
I am having trouble with this question. For y > 1, the value of cosec [arccos (1/y)] is?
Penny Nom lui répond.
The average rate of change 2008-03-29
Tom pose la question :
For the function x/3x-1 find the average rate of change between the interval x=1 and x=5?
Harley Weston lui répond.
A function satisfying f(x) + 2f(1/x) = x 2008-03-25
Joan pose la question :
Let f be a function satisfying f(x) + 2f(1/x) =x for all real numbers (x does not equal 0)
a) Find f(1) justify your answer

b) Find f(2) justify your answer

Penny Nom lui répond.
Inverses of functions 2008-03-13
jess pose la question :
if g(x)=2x+3 find g^-1(g(4)) how do I sovle I cant's figure out what to do with the 4
Stephen La Rocque lui répond.
Saving to buy a coat 2008-03-09
alayna pose la question :
Jackie is saving her money to buy a coat that costs $121. If she already has $61 and saves $15 each week, in how many weeks can she buy the coat ? Make a function table to answer the question.
Penny Nom lui répond.
Composition of functions 2008-03-07
sharon pose la question :
Find FoG(x)
F(x)= the square root of x-9
G(x)= x^2
and also find GoF and their domains

Penny Nom lui répond.
F( x - 2) = (x + 3)/ (x - 4) 2007-12-20
Sean pose la question :
If F( x - 2) = (x + 3)/ (x - 4) , then F(5) = 10/3

How do you solve this problem and what section of calculus can I learn the technique to solve this type of problem?

Stephen La Rocque lui répond.
Transformations and compositions 2007-11-29
mary pose la question :
Is there any possible relationship between composite functions and the concept of function transformations?
Harley Weston lui répond.
Maximize his profit 2007-11-12
apoorva pose la question :
During the summer months Terry makes and sells necklaces on the beach. Last summer he sold the necklaces for $10 each and his sales averaged 20 per day. When he increased the price by $1, he found that he lost two sales per day.

a. Find the demand function, assuming it is linear.
b. If the material for each necklace costs Terry $6, what should the selling price be to maximize his profit?

Penny Nom lui répond.
Family of functions 2007-11-12
Russell pose la question :
Consider the family of functions
f(t)= Asin3t + Acos3t +Bsin8t + Bcos8t

find exact values of parameters A and B so that f(0) = 2 and f ' (0) = 1

Stephen La Rocque lui répond.
Domain and range 2007-10-12
Dawn pose la question :
Hi, I've been out of school for 8 years and recently picked up a math correspondence course. I'm having trouble trying to figure out the range and domain of a linear function. I've read everything I can find in my text, lessons and on your site and I still can't figure out what I'm suppose to be doing. The function is y=2x+1. Please help.
Penny Nom lui répond.
Inverses of Quadratic Functions 2007-10-11
Elliot pose la question :
I'm a special education tchr trying to demonstrate how to find the inverse (using algebra) of quadratic functions. Any help would be greatly appreciated.
Steve La Rocque and Harley Weston lui répond.
The average rate of change of a function 2007-10-11
vern pose la question :
Find the average rate of change of the function over the given interval. Compare this average rate of change with the instantaneous rates of change at the endpoints of the interval. f(X)=sinX for the inverval [0,pi/6]?
Harley Weston lui répond.
Maximizing profits II 2007-10-05
a student pose la question :
Suppose there are three firms with the same demand function. The function is Q=1000-40P. Each firm also a a cost function.
Firm 1: 4000+5Q, Firm 2: 3000+5Q, Firm 3: 3000+7Q.
What price should each firm charge if it wants to maximize profits.

Harley Weston lui répond.
Irrational functions 2007-10-01
alicia pose la question :
i have a question about irrationals functions.
i have been using them quite some time now, but i wonder where they can be found in daily life?
i hope you can help me,

Harley Weston lui répond.
Is x/y + y/x = 2 a function? 2007-09-06
Farzan pose la question :
Is x/y + y/x = 2 a function or not.
Penny Nom and Stephen La Rocque lui répond.
Relations and functions 2007-08-16
virginia pose la question :
determine whether each relation is a function provide reasons for identifying relation
(3, 4) (5, 9) (9, 9) (2, 3)
(0, 0) (0, 1) (1, 4) (2, 4)
(2, 1) (4, 5) (8, 4) (1, 0)
(8, 3) (8, 0) (7, 7) (4, 7)

Steve La Rocque lui répond.
The domain and range of a quadratic function 2007-07-17
Linda pose la question :
I have been trying to solve this problem but I'm unable to figure it out. How do I find the domain and range of y=-(x+1)^2-3? Please explain...thanks!
Stephen La Rocque and Penny Nom lui répond.
Trig functions for angles not between 0 and 90 degrees 2007-07-16
Tim pose la question :
My question: Why is the value of a trigonometric function, the same, for an angle over 90 degrees and its reference angle? How are the angle and its reference related? Do they both form a triangle that has equal sides?
Penny Nom lui répond.
Derivative of a Function 2007-07-09
Bob pose la question :
What is the derivative of the function a sub n = [n/(n+1)]^n ?
Stephen La Rocque lui répond.
Period of a sum of trig functions 2007-06-17
Aakash pose la question :
the period of the function f(x)=cos3x+sin4x+tan4x
Stephen La Rocque lui répond.
Express a certain variable as a function of another variable 2007-06-12
Gilligan pose la question :
The volume V of a right circular cone is V = (1/3)pi(r^2)(h). If the height is TWICE the radius, express the volume V as a function of r.
I see the phrase "express a certain variable as a function of another variable" a lot in math books. What exactly does that mean? Is there another way to say the same thing?

Stephen La Rocque lui répond.
Composition functions 2007-06-12
Gilligan pose la question :
Find functions f and g so that f(g(x)) = H.
(1) H(x) = (1 + x^2)^(3/2)
(2) H(x) = int(x^2 + 1)
I don't know where to start.

Stephen La Rocque lui répond.
The limit of a rational function 2007-05-28
Imad pose la question :
     3 _______ 3 _______
lim \/ 1 + x -    \/ 1 - x
x->0 ---- ----------------------------
              x

Penny Nom lui répond.
What does inverse graph represent? 2007-03-30
san pose la question :
what does inverse graph represent?
Penny Nom lui répond.
Is the inverse of a function always a function? 2007-03-29
San pose la question :
Is the inverse of a function always a function? Please justify. Thank You!
Penny Nom lui répond.
What makes a relation a function? 2007-03-21
san pose la question :
What makes a relation a function?
Haley Ess lui répond.
An even function 2007-03-07
Dana pose la question :
Find a function t(x) such that t(x)/x+3 = y is an even function
Haley Ess lui répond.
An odd function 2007-03-06
Dana pose la question :
If g(x) has a domain of all real numbers, name one point on a graph and explain why it must be there. g(x) is an odd function.
Penny Nom lui répond.
Finding the x-intercept 2007-03-02
Ash pose la question :
Y = -1/100X^2 =27/10X +0 = 0 THE Y INTERCEPT IS 50 HOW DO I FIND THE X INTERCEPT
Gabriel Potter lui répond.
y = f(x) and y = 2f(x-6) 2007-03-02
carl pose la question :
if P(4,-5) is a point on the graph of the function y=f(x), find the corresponding point on the graph of y=2f(x-6).
Penny Nom lui répond.
Input-output table 2007-01-10
Richard pose la question :
Question is make an input - output table for the function using the domain 0,1,2,3,4, Then state the range of the function.

y =x + 8 ?

y =0.4x +3 ?

Penny Nom lui répond.
y = 5 x - 3 2007-01-10
Richard pose la question :
Question is the function y = 5 x - 3 for the given value of x 7 , 1 or 4
Stephen La Rocque and Penny Nom lui répond.
Composition of functions 2006-11-19
RJ pose la question :
Let f0(x) = 2/2-x and fn+1 = f0 o fn for n greater than or equal to 0. Find a formula for fn and prove it by mathematical induction. Recall that o represents function composition. i.e., (f o g)(x) = f(g(x)).
Stephen La Rocque lui répond.
Composition of functions 2006-11-18
Oryan pose la question :
Given f(x)=-2x^3 and g(x)-4x-5, find g(f(-1))
Stephen La Rocque lui répond.
Piecewise functions 2006-11-08
Kait pose la question :
We discussed how to graph piecewise functions today and I'm very lost!! I'm sitting here staring at this problem that says:
f(x){2x+1, if x <1
f(x){-x+4, if x is greater than or equal to 1.

Penny Nom lui répond.
Piecewise functions 2006-09-24
Claudia pose la question :
hi! i was just looking at a question by someone else about piecewise functions, but i still don't get it.
my problem is
g(x){x+2 if x <-2}
g(x){2x - 1 if x> or = -2}

Penny Nom lui répond.
The zeros of a function 2006-06-12
Sky pose la question :
find all the real zeros of the function:
f(x)=2x3 + 4x2 - 2x - 4

Stephen La Rocque lui répond.
Geometric sequence and basic functions (graphs) 2006-04-20
Marlene pose la question :
Which of the basic functions is related to the geometric sequence: Linear, Quadratic, Rational, or Exponential? Can you give me an example of how it would be used in normal life?
Stephen La Rocque lui répond.
Finding the inverse of a function 2006-04-12
Sam pose la question :
If g(x) = 2x+3/5 then how do I find the inverse?
Walter Whiteley lui répond.
An exponential function 2006-04-03
Meadow pose la question :
The graph of an exponential function passes through the points (0,1) and (4,10) find the constant of growth or decay. State the function.
Stephen La Rocque lui répond.
Piecewise functions 2006-03-21
Kris pose la question :
First Problem:
Southeast Electric charges .09 cents per kilowatt-hour for the first 200 kWh.The company charges .11 cents per kilowatt-hour for all electrical usage in excess of 200 kWh. How many kilowatt-hours were used if a monthly electric bill was $57.06? The answer I came up with is 360, is that right? and also how do I set it up in an equation form?

Second Problem:
A construction worker earned $17 per hour for the first 40 hr of work and $25.50 per hour for work in excess of 40 hr. One week she earned $896.75. How much overtime did she work? I came up with 8.5 hrs over-time worked. Again I don't know how to set up the equation to come up with the answer.

I need some pointers on how to figure out story problems! If you have any suggestions that would help me out I would be very grateful.

Penny Nom lui répond.
sinh(i/2) 2006-02-09
Louis pose la question :
How can you set up an equation to find sinh(i/2)
Penny Nom lui répond.
fog 2005-11-12
Janice pose la question :
I am having problem with the (fog) function

(fog) (x). Given f(x)= 2x2 ; g(x)= 3-4x

Penny Nom lui répond.
Painter's caps 2005-10-19
Duk pose la question :
The equation C=10 +2n represents the cost in dollars, C, for n painter's caps advertising the walkathon. Which pair of values could represent a number of caps and the cost for that number of caps, (n, C)?

(0, 10) (7, 24) (15, 30)

Penny Nom lui répond.
A piecewise function 2005-09-15
Duncan pose la question :
A child is assigned to your care and she has a headache. The parent has authorized the administration of Children's Tylenol. Read a box of Children's Tylenol (or any other similar drug) and find the directions for administration. Note the child's weight and the corresponding dosage. (Be sure the drug you choose has a minimum of 4 weight intervals.)
Penny Nom lui répond.
y = log(x) + x. Solve for x. 2005-08-26
Alain pose la question :

I have the following equation:

y = ln(x) + x

How do I solve for x?


Penny Nom lui répond.
Labour efficiency 2005-08-23
Rob pose la question :

The problem, on the surface, seems very simple and yet has created some controversy among a group of accountants. The problem itself has to do with labour efficiency rates and only involves two variables; standard working hours, and actual working hours. The difficulty lies in deriving an efficiency % from these two numbers.

Standard working hours or the targeted number of labour hours required to produce one widget, which I will represent as "s". Actual working hour or the actual number of labour hours require to produce one widget, which I will represent as "a". Labour efficiency I will represent with "E". The prevailing calculation with which I have a problem with is this:

s/a=E or if s=3000, and a=4000 then 3000/4000=75%

What bothers me about the calculation is that the standard hours get represented as a percentage of the actual hours and in my opinion changes the focus of the calculation from standard or target, where it should be, to the actual hours. I cannot define why, but this just seems inherently wrong to me.
The calculation that I use:

(1+((s-a)/s))=E or if s=3000, and a=4000 then (1+((3000-4000)/3000))=66.67%

My calculation is like a %change from standard calculation. However, there is something that also concerns me about my calculation.

If you substitute 100 for a and 50 for s, then you come to a quandary, because if you plug those numbers into the second equation the result is of course zero % efficient which doesn't sit right with me either. If you plug them into the first calculation you get 50% efficiency which doesn't really seem to work either, because you require 100% more hours to do the same work in this case. ???

Is the first calculation correct? Am I missing something altogether? Are both calculations off base?


Harley Weston lui répond.
The range of a function 2005-08-21
Kelsey pose la question :
What is the range of the function f(x) = 4x - 6 when the domain is {-3,-1,1,3,5}?
Penny Nom lui répond.
Rational functions 2005-04-05
Nicole pose la question :
My name is Nicole and I am a teacher at Weyburn Comprehensive School. I am currently teaching both Math B30 and Calculus 30 at the school and I have a question about rational functions. I know that if a rational function (by definition) has common factors in the numerator and the denominator then it is not a rational function (math b30) however in calculus this common factor creates a hole in our graph. Can you explain to me why a common factor or constant does not give us a rational function?
Penny Nom and Leeanne Boehm lui répond.
Profit 2005-01-10
Abraham pose la question :
The profit a coat manufacturer makes each day is modeled by the equation P(x)=-x2+120x-2000, where P is the profit and x is the price for each coat sold.For what values of x does the company make a profit?
I don 't understand this problem(how to do it) and hope you can help me.

Penny Nom lui répond.
The points of intersection of two graphs 2004-11-05
Benjamin pose la question :
How do I find the points of intersection of the two functions:
1) y =
2 - e-x 2) y = 1 + x2

Harley Weston lui répond.
f(x) = x-4 if x<2 2004-09-21
Dani pose la question :
Hi, my name is Dani. I'm in tenth grade Algebra 2, and I'm learning about a lot of different kinds of functions, and I can't quite seem to understand how every part of the piecewise function works. I understand most of it, I think, but I've been looking at an example in my math book, and I'm not sure how they got the answer they did. The part I don't understand reads: "Graph f(x) = x-4 if x<2" and "Identify the domain and range." The picture in the book shows an open circle at (2,-2), with an arrow going down and to the left with the slope being one. How did they get the open circle to be at (2,-2), and why does the arrow point where it does?
Penny Nom lui répond.
An inverse 2004-09-09
Hillary pose la question :
I cannot figure out the inverse of this function.
f(x)= 1/2x -1

Penny Nom lui répond.
Limits and composite functions 2004-08-07
Sue pose la question :
I have two questions, one about a limit and the other about a composite function. If you could help me, I'd really appreciate it.

1. Find the limit:

lim[x->0] (x*csc(x))

I converted csc(x) to cos(x)/sin(x), but I didn't know what to do after that.

2. f(g(x)) = ln(x^2 + 4), f(x) = ln(x^2) and g(x) > 0 for all real x, find g(x):

I'm having trouble with this one because x^2 + 4 isn't a perfect square.

--Sue

Penny Nom lui répond.
The intersection of two graphs 2004-07-28
JJ pose la question :
Is there a way to find the intersections of these graphs algebraically?

x^2 + y = 4 & 2x - y = 1

I got (1.45, 1.9) and (-3.45, -7.9) with a graphing calculator.

AND THESE...

y = 3.29x & y = 5.5(x^0.5)+ 10000

I got x at 3133 with a graphing calculator.

Penny Nom lui répond.
The inverse of a quintic function 2004-07-22
A student pose la question :
I'm really having trouble finding out the inverse of this quintic equation. F(X)= X5+3X3+1.I know that this quintic has an inverse because it is one to one. But I can't find a method to solve this. Finding the inverse of a quadratic or a cubic equation is a lot easier, but with this quintc I am really lost. I even know how the graph of this equation and its inverse looks like, but I'm not sure if Iam getting the right equation. Please help me out.
Penny Nom lui répond.
A probability density function 2004-04-14
A student pose la question :
The label on a bottle of liquid detergent shows contents to be 12 ounces per bottle. The production operation fills the bottle uniformly according to the following probability density function:

f(x) = 8 for 11.975 <= x <= 12.10
and
f(x) = 0 elsewhere

a. What is the probability that a bottle will be filled with 12.02 or more ounces? b. What is the probability that a bottle will be filled between 12 and 12.05 ounces? c. Quality control accepts production that is within .002 ounces of number of ounces shown on the container label. What is the probability that a bottle of this liquid detergent will fail to meet the quality control standard?

Penny Nom lui répond.
Polynomials 2004-01-25
Bruce pose la question :

A polynomial is defined as
Polynomial functions are functions that have this form:
f(x) = anxn + an-1xn-1 + ... + a1x + a0
The value of n must be an nonnegative integer. That is, it must be whole number; it is equal to zero or a positive integer.
The coefficients, as they are called, are an, an-1, ..., a1, a0. These are real numbers.

Questions:

  1. why must n be positive?
  2. what are some historical facts about the evolution of the definition?

Harley Weston lui répond.
Finding angles 2003-12-02
Jason pose la question :
I AM TRYING TO SOLVE A TRIG PROBLEM AND HAVE FORGOT HOW TO DO IT. WHAT I HAVE IS A RIGHT TRIANGLE WITH SIDE A BEING 14 FEET AND SIDE B BEING 3 FEET, USING PYTHAGOREAMS THEOREM SIDE C SHOULD EQUAL 14.318 FEET ON A RIGHT TRIANGLE BUT I AM TRYING TO REMEMBER HOW TO FIND MY ANGLES OTHER THAN THE ONE THAT IS 90 DEGREES.
Penny Nom lui répond.
A parabola 2003-10-24
Delores pose la question :
Given the vertex (4, -2) y intercept = -6 find if/where the parabola crosses the x axis?
Penny Nom lui répond.
Domain of a function 2003-10-14
Karim pose la question :
Find the Domain of the Function
H(x) = Log3 (4x + 7)-10
H(x) = log base 3 times 4X plus 7 minus 10
i am having problem solving these kinds of problems.

Penny Nom lui répond.
Graphing a piecewise function 2003-08-24
Amber pose la question :
How do i begin to graph a piecewise function, absolute function or step function?
Penny Nom lui répond.
A rule with a variable 2003-08-24
Crystal pose la question :
what is a rule with a variable
Penny Nom lui répond.
Two precalculus problems 2003-08-04
Kate pose la question :

Please help me verify the identity:
cos2x(sec2x-1)=sin2x

Also I am having trouble withdetermining whether f(x) is odd, even, or neither
f(x)=x3-x


Penny Nom lui répond.
The domain of 1/g(x) - 5 2003-07-03
Barbara pose la question :
If the range of g(x) is ( neg. infinity,4] and the domain of g(x) is ( neg. infinity, infinity), how do I find the domain of 1/g(x) - 5?
Penny Nom lui répond.
y = 1 - sin(x + 60) 2002-12-10
Eman pose la question :
Sketch the graph of y = 1 - sin(x+60). for 0 <= x<= 360, giving the coordinates of the maximum and minimum points and the pints where the curves crosses the y axis.
Penny Nom lui répond.
A function that is onto but not one-to-one where f:N-->N 2002-12-06
Lisa pose la question :
A function that is onto but not one-to-one where f:N-->N
Penny Nom lui répond.
Performance reviews 2002-11-21
Lara pose la question :
Perhaps you can help.

He's doing performance reviews at work.

The average performance review is 3.92 on a 5.0 scale. This person would receive a 3.5% raise for next year.

The highest performance review is 4.9 and this person would recieve a 6.0% raise for next year.

How do I solve for the other performance review numbers.


Penny Nom lui répond.
Differentiating inverses 2002-11-20
Amy pose la question :
f(x)= x3+x+1, a=1 find g'(a) (g = f -1). I am having trouble finding g(a).
Penny Nom lui répond.
A functional equation 2002-10-14
Rob pose la question :
Let f be a function whose domain is a set of all positive integers and whose range is a subset of the set of all positive integers with these conditions: a) f(n+1)>f(n)

b) f(f(n))=3(n)

Claude Tardif lui répond.
A linear function 2002-09-09
Chad pose la question :
If y = 9x - 13 does it represent a linear function? And if it does what is its slope and is it a direct variation?
Peny Nom lui répond.
Domain of a function 2002-07-20
Andy pose la question :
I'm having difficulty in finding the domain of

1/(x2 -2x + 4)

one over x squared minus 2 x plus 4.


Penny Nom lui répond.
Functions and relations 2002-04-25
Erin pose la question :
Here's a few math problems that might drive a person insane ;)
  1. If 2f(x) - 3f(1/x) = x^2 what is f(2)?

  2. What are the domain and range of the following relations?
    • x^2 - 4y^2 = 25
    • 4x^2 + 9y^2 = 36

  3. The port of Swan Harbor is 200km away from Merry Town Inlet on a bearing of N50E from Merry Town. A ship leaves Merry Town at 8am and sails N15W at 15 km/h. At the same time, a second ship leaves Swan Harbour on a course of S80W at 20km/hour. How close, to the nearest km, are the two ships at 13:00?

  4. Prove the identity. 1+sinx + cosx/ 1-sinx + cosx = 1+sinx / cosx

Penny Nom lui répond.
Composition of functions 2002-04-06
Yvonne pose la question :
In our new text book, the following question occurs: State the domain and range of g(f(x))given that f(x) = -x2 - 4 and g(x) = sqrt(x)

The range of f(x), x<=-4, is the domain of g(x). BUT, there is no solution in the Real numbers for g(f(x))= sqrt(-x2 - 4).

In the solutions it says that this is not a function and therefore does not have a domain or range. Is it a relation? Is it anything?


Claude Tardif lui répond.
Zeta[2]=(Pi2)/6 2002-02-02
alex pose la question :
Can you please tell me a proof that Zeta[2]=(Pi2)/6
Chris Fisher lui répond.
Catenary 2002-01-02
Jason pose la question :
I am a high school math teacher. I was asked by a friend who is in architectural design for a method for determining the volume of what he called a Catenary.

The Catenary curve is modeled by the equation y=a cosh(x/a). I ran into a mess when I tried to compute the volume of the solid formed by revolving that curve around the y-axis.

Any help you can provide would be greatly appreciated.


Harley Weston lui répond.
Composition of functions 2001-12-16
Paula pose la question :
  1. if f(x)= 3x-1 and g(x)= 1/2x + 3 find fog(2)

  2. find the values of x for which tanx=0

Penny Nom lui répond.
Dual spaces 2001-11-26
Hoda pose la question :
In the book "Linear Functional Analysis" from Epstein there is a proof (page 116) of the following theorem:

The dual space of Lp is equal to Lq.

Later, it is stated as a theorem without proof that

for 1 <= p < +infinite, The dual space of lp is equal to lq.


Doug Farenick lui répond.
Some functions without numbers 2001-11-16
A student pose la question :
I have a worksheet that is about functions. It doesn't only use numbers. I need help to figure out the function and the solution to how the answer is solved.
Claude Tardif lui répond.
Symmetry of f(x) = ax^n 2001-10-18
Mohammed pose la question :
a function of the form f(x)=axn, where a doesn't equal 0 and n is a positive integer is called a power function . how is the exponent in the equation of a power function related to the symmetry of its graph?
Penny Nom lui répond.
A function or not a function? 2001-10-18
Christian pose la question :
Which are the following are not functions?
  1. y = x2

  2. y = x3

  3. x = y2

  4. y = 3

Leeanne Boehm lui répond.
Inverting a function 2001-09-30
Brandie pose la question :
Could you please tell me what is the basic guideline for inverting a function

Example:
S(R)=2PiRal
V(R)=PiR(squared)bl
R(V)=?


Claude Tardif lui répond.
A quadratic function 2001-05-10
A parent pose la question :
A quadratic function is given by f:x------ax2+b

If the two points A(2, 2) and B (0, -8) are on the graph of the function, then find a and b.

Penny Nom lui répond.
National consumption function 2001-05-09
Brian pose la question :
If consumption is $11 billion when disposable income is 0 and the marginal propensity to consume is dC/dy = 1/(2y+4)1/2+0.3(in billions of dollars), find the national consumption function.
Harley Weston lui répond.
The average value of a continuous function 2001-05-08
Esther pose la question :
The average value of a continuous function y = f(x) on the interval [a,b] is given by ________________?
Harley Weston lui répond.
A sequence defined recursively 2001-05-01
A student pose la question :
A sequence s is defined recursively as follows:

s0=1
s1=2
sk=2sk-2 for all integers

- Compute s2,s3,s4... to guess an explicit formula for the sequence sk.
Penny Nom lui répond.

Choosing a car 2001-04-28
Ashley pose la question :
THE CAR DEALERSHIP IN TOWN OFFERS 32 DIFFERENT MODELS OF VIHICLES.EACH MODEL HAS A CHOICE OF EIGHT INTERIOR COLORS,EIGHT EXTERIOR COLORS,AND ALSO THE OPTION OF AUTOMATIC OR MANUAL TRANSMISSION. HOW MANY COMBINATIONS ARE POSSIBLE?
Penny Nom and Andrei Volodin lui répond.
The domain of a function 2001-04-08
Mina pose la question :
Let f(x) = (2x2+3x-17)/(x+5)
What is the domain of f? What are the values of x for which f'(x) does not = 0?

Harley Weston lui répond.
f(x), f(x) + 2, f(x +2) 2001-04-04
Monica pose la question :
Could you explain to me how one should go about graphing functions such as f(x), f(x+2), and so on. Also, how should you explain things such as constants and relationships among functions?
Penny Nom lui répond.
Domain and Range and Zeros 2001-02-27
Beth pose la question :
1. f(x)=15-2x-x2

2. g(t)=square root of 4-t2

3. y=t-3/t2-t-6


Penny Nom lui répond.
Adding functions 2001-02-19
Jackie pose la question :
f(x) = x2 + 1; g(x) = x2 - 1

find
a) ((f+g) of h)) (x)
b) ((f-g) of h)) (x)
c) ((f of h) - (g of h)) (x)


Penny Nom lui répond.
Range of a function 2000-11-21
David Bell pose la question :
Given a rational function such as f(x) = (8x-3)/(4x-1). How can the range be found.
Penny Nom lui répond.
Domain of a function 2000-11-15
Mickey pose la question :
state any restrictions on the domain of the function.

y = 5x - 12 over 27x + 6 x does not equal what________?


Penny Nom lui répond.
Graphing F(x) = 3x 2000-11-06
Jose pose la question :
graph the exponential problem F(x)=3x
Harley Weston lui répond.
An equation involving x to the x 2000-07-22
Joy Peter pose la question :
I am joy, a teacher teaching Maths at the secondary level and while solving a sum came to this stage when i got xx (1 + log x) = 0, by which we can conclude that xx = 0 or 1 + log x = 0. If xx = 0, than what should be the value of x? I feel that the value of x should then be 0 (zero) but then how do I explain this to the students as we also know that anything to the power of 0 is 1 but here 0 raised to 0 is 1. If this is not defined then how do I explain this?
Penny Nom lui répond.
Calculus Research Questions 2000-05-22
William Wright pose la question :
I am a Calculus Teacher, and me and my class ran into these two problems without solutions in my manual, we got answers, but are unable to check them. If anyone gets this email and can respond to this with the solutions it be greatly appreciated.
.
.
.

Harley Weston lui répond.
Graphing a linear function 2000-05-17
Chelsea pose la question :
I need help with grahing linear functions.If you could e-mail me back the basics and how tos I would be much appriciative.
Penny Nom lui répond.
sin(7pi/12) 2000-05-04
Kristel pose la question :
What is the exact value of sin 7pi/12?
Chris Fisher and Paul Betts lui répond.
Graphing cube roots 2000-04-27
Heather Jones pose la question :
What do the graphs of cube roots look like?
Walter Whiteley lui répond.
Functions that satisfy f' = f 2000-03-16
Kevin Palmer pose la question :
Recently my calculus teacher asked his students to try and find any functions whose derivatives where the exact same as the original function.

The only function then I have determined that statement to be accurate in is all the natural exponential functions. Ex. f(x) = ex, f'(x) = ex

If possible could you please email me all the functions that you can find in which the original function and its derivative is identical.


Claude Tardif lui répond.
Irrational algebraic functions 2000-02-21
Bucky Cadena pose la question :
Here is the multipart problem:

Given f(x) = x-3* squareroot of x + 4

What does the f(x) intercept equal Find the two values for which f(x) = -5 Find the one value for which f(x) = -3


Harley Weston lui répond.
Functions 2000-01-23
Tara pose la question :
Hi my name is Tara, I have two math problems that I need help with in my calculus math class.

  1. If f(x)= x - 2 show that (x+3)f(x)-(x+2)f(x+1)+4=0

  2. Graph this function and use the graph to determine the range y=2x2 - 8x - 3

Harley Weston lui répond.
The limit of f(x)/x 2000-01-22
Laurent Jullien pose la question :
I would appreciate help to prove that a twice continuously differentiable convex function from R+ to R has the property that f(x)/x has a limit when x tends to infinity.
Claude Tardif lui répond.
Domain of a function 2000-01-19
Stacey Hutchison pose la question :

What is the domain of:

f(x) = -1/(x + 4)


Patrick Maidorn lui répond.
Functions 2000-01-06
Tori Morris pose la question :
Consider the function f(x)=x2-3. Which of the following are true?

  1. f(1)>f(0)
  2. f(2)>f(-3)
  3. f(2)=f(-2)
  4. f(-1)=f(3).
More than one answer can be true.

Penny Nom lui répond.
Period 1999-12-28
Mahdawi pose la question :
I have attached a diagram of the graph, and I need to find out its period. I really don't understand how to do so, please help!
Harley Weston lui répond.
Three algebra problems 1999-12-28
Stephanie Branton pose la question :
  1. If P represents the product of all prime numbers less than 1000, what is the value of the unit's digit of P?

  2. Do any real numbers a and b exist such that: ln(a+b)=ln a + ln b? if so, what are they?

  3. Define a function by: f(x)=1/1-x where x is not equal to 0,1. what is f(f(f(a)))?

Harley Weston lui répond.
Graph of a sine function 1999-12-23
Pierre pose la question :
Given;
amplitute:1
period: 540
Phase shift: 60 degree,right

I am ask to right the equation: sin 2/3 (value -60degree)

When I am asked to graph the equation, the period is mixing me up.
Harley Weston lui répond.

polynomial functions 1999-11-19
Quinn pose la question :
  1. Without fully factoring the following show that they all have the same zeros:

    I: x4-x2+2x+6
    II: -x4+x2-2x-6
    III: -4x4+4x2-8x-24
    IV: 10x4-10x2+20x+60

  2. When P(x)=x3-3x2+5x+1 and G(x)=x3-2x2-x+10 are each divided by(x-a) the remainders are equal. At what coordinate point does the graph of P(x) intersect G(x)?

Walter Whiteley lui répond.
Domain and Range of a Function 1999-11-14
Michelle Mellott pose la question :
How do you find the range of the following function:

2y2/(y2+5y+6)??

I know the domain is x not equalled to -2, -3. How can one easily find the range?
Harley Weston lui répond.

Inverses of functions 1999-11-01
Leanne Hickey pose la question :
Let f(x) = 2x2 -3x + 2. Find f-1(4) given the fact that f(2) = 4. So the question is finding the inverse of 4, he said it's easier than it looks.
Penny Nom lui répond.
Piecewise functions. 1999-10-20
Jenny pose la question :
How do you figure out a piecewise function by hand?

e.x.
( 2x (if x is not equal to 0)
f(x)=<
( 0 (if x is not equal to 0)
Harley Weston lui répond.

Even and Odd Function 1999-06-17
Kent pose la question :
There is one function with the domain of all real numbers that is both even and odd. Please give me the answer to this question before I go insane.
Penny Nom lui répond.
Points on a Graph 1998-10-03
Nouver Cheung pose la question :
If the point P(-3,2) is on the graph of y=f(2x-1), what point must be on y=f(x)-3?
Harley Weston lui répond.
Polynomials 1998-01-13
Sarah Storkey pose la question :
Hi, My name is Sarah, My question is at the junior level.

My question is, what is a polynomial?
Harley Weston lui répond.

The Range of a Function. 1997-09-12
Karel Marek pose la question :
Math Is Book 6 (Ebos/Tuck) question 5(b) gives a surprising answer at the back of the book..

The question is:
Indicate the domain and range for this: y = sqr(x-9) (Square root of)

The answer for the domain is x>=9 which is not surprisingly, but the range is y>=0, yER ... which I could understand if you were not allowed to transform the equation into x as the subject..

But all example on the facing page DO TRANSFORM the equation at will with x and/or y as the subject..

Can you explain this...
??
Chris Fisher lui répond.

Square Roots and Functions. 1997-04-23
Ed pose la question :
1. In most texts the solution to a question such as square root x = -6 is

x is undefined.

Yet when teaching to solve
xsquared = 36
x = +6 or -6

There appears to be a contradiction here. My question is when, where and why do we use the principle square root, not both + and -? This often occurs as the extraneous root in the solution of radical equations and in stating the domain and range of functions involving square roots.

2. Are there any simple rules for determining whether equations are functions without graphing them and doing a vertical line test?
Harley Weston lui répond.

A Functional Equation. 1997-02-26
Ronald Lui pose la question :
Find all functions f:S --> S statisfying the two conditions:

1)f(x+f(y)+xf(y))=y+f(x)+yf(x) for all x and y in S

2)f(x)/x is strictly increasing on each of the interval -1
Saroop Kaul and Chris Fisher lui répond.

Grade nine problem solving 1996-03-11
Azmat Hussain pose la question :
Can math problems be actually fun and engaging?
Diane Hanson lui répond.
 
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