Number of results: 20,563

**Calculus (Derivatives of Inverse Functions)**

Suppose f(x) = sin(pi cos(x)). On any interval where the inverse function y = f^-1(x) exists, the derivative of f^-1(x) with respect to x is: I've come as far as y = arccos ((arcsin(x))/pi), but I am not certain this is right.

*March 15, 2012 by Mooch*

**Pre Calculus**

Inverse functions what is the inverse function of f(x)=1/square root of x +1? and f(x)=1-x^2, x<0?

*October 23, 2011 by Josh*

**calculus - derivatives**

can you please find the first 5 derivatives for: f(x) = (0.5e^x)-(0.5e^-x) f'(x) = ? f''(x) = ? f'''(x) = ? f''''(x) = ? f'''''(x) = ? thanks :) f(x) = (0.5e^x)-(0.5e^-x) f'(x) = 0.5 e^x + 0.5 e^-x f''(x) = 0.5 e^x - 0.5 e^-x f'''(x) = 0.5 e^x + 0.5 e^-x f''''(x) = 0.5 e^x - 0...

*July 30, 2007 by COFFEE*

**Calculus**

F(x) = 1-x and g(x) = 1/x These functions have the property that f = f^-1(inverse) and g = g ^-1. That is, the inverse of f is equal to itself and the inverse of g is also equal to itself. Take the composition of each function with itself to show that this is true. Remember, ...

*September 23, 2011 by Scooby16*

**calculus**

Find the derivatives of the functions k(x)=(x^3+e^x)^4

*February 11, 2013 by Joe*

**Math - Inverse Functions**

Find the inverses of the following functions. y = 3(x - 1)^2, x >= 1 Work: x = 3(y - 1)^2 x = 3(y - 1)(y - 1) x = 3(y^2 - y - y + 1) x = 3y^2 - 6y + 3 And now what do I do!? Please explain and show me how to solve this inverse function! ... Thank you

*January 10, 2008 by Anonymous*

**Calculus-Inverse Functions**

is the inverse function of x+ floor(x) equal to x - floor (x/2) i got this after plotting points but i'm not sure. thank you

*March 31, 2013 by Matthew*

**Advanced Algebra**

What is the inverse of each of the functions defined by the following equations, if the inverse exists. If the inverse does not exist for the largest possible domain, limit the domain so that the inverse will exist. In each case, give the domain and range of both the function ...

*November 15, 2014 by Keith*

**Calculus**

Find the outside and inside functions of the following to find their derivatives: 1) sqrt(2x+9) 2) cos(cos(x)) 3) tan(x) I already know how to find their derivatives I'm just not exactly sure what parts of the chain rule equation would be considered the outside and inside.

*June 18, 2013 by Robin*

**Calculus: Derivatives**

I'm having trouble understanding what derivatives in calculus (instantaneous speed) is. Can someone please explain it to me, or provide some easy links to learn from? Thanks!

*September 9, 2007 by Joe*

**Calculus**

Hello, I really need help on these two homework problem. >< In problem #1, I believe it is related to the exponential functions and their derivatives section...in Calculus II? So, surely there should be a ln in the solution as well? I would like a step by step process ...

*January 31, 2015 by Aria*

**graph!**

how can the graph of f(x)= X^2-4X be used to obtain the graph of y=g(x) ?????? don't know can you help me out? What is g(x)? The inverse function of f(x)? http://www.uncwil.edu/courses/mat111hb/functions/inverse/inverse.html

*September 4, 2006 by kris!*

**Calculus**

[Inverse Functions] f(x)= 5cos(x)sin^(-1)(x) f'(x)=?

*October 7, 2009 by Z32*

**Pre-Calculus**

Find the inverse function for the function f(x)=2^(x)+1/2^(x)-1 You will need to use some properties of logarithmic functions to find the inverse of this particular function.

*April 30, 2013 by Thomas*

**Math**

If the inverses of two functions are both functions, will the inverse of the sum or difference of the original functions also be a function? Explain your reasoning.

*November 28, 2016 by Anonymous*

**Advanced Functions 12**

A student writes, "The inverse of y = -√(x+2) is y = x^2 - 2." Why is this statement false? I don't understand how it isnt the inverse. The textbook says that changing the domain will make it the inverse? Wouldn't that only make it a function?

*September 17, 2016 by y=1/0*

**Calculus III**

Derivative of Inverse Trigonometric Functions f(x) = sin(arccos(4x)) What is f'(x)?

*January 22, 2008 by Sean*

**Calculus III**

Derivative of Inverse Trigonometric Functions f(x) = cos(arcsin(2x)) What is f'(x)?

*January 22, 2008 by Sean*

**Calculus**

find the derivatives of the given functions. g(t)=sqrt t(1+t)/t^2 the sqrt is just over t.

*February 4, 2013 by Mike*

**Calculus**

Find the first and second derivatives of the given functions. y=¡î(x©÷+1) y'=x(x©÷+1)^(-1/2) y"=[1(x©÷+1)^(-1/2)]-[(1/2)[(x©÷+1)^(-3/2)](2x)(x)] y"=[(x©÷+1)^(-1/2)]-[(x©÷)(x©÷+1)^(-3/2)] Is the second derivative right?

*November 10, 2009 by sh*

**CALCULUS**

show that f(x) = x^2-1 (x is greater than and equal to 0) and g(x) = root(x-1) (x is greater than and equal to -1) are inverse functions. when i try f(g(x)) = x and g(f(x)) = x to show that the two functions are inverses it doesn't work because i am not left with x when i ...

*February 15, 2009 by joey*

**Linear Algebra**

which of the following functions is the inverse of F(X)=3x F(X)=-3X F(X)=X (cubed)**** F(X)= X/3 This function does not have an inverse. Thank you!

*December 22, 2016 by Who would know*

**Calculus Can you help**

Suppose the functions f and g and their derivatives have the following values at x = 1 and x = 2. Let h(x) = f(g(x)). Evaluate h′(1). X | f(x) G(x) f'(x) g'(x) ____________________________ 1 | 8 2 1/3 -3 2 | 3 -4 2π 5 My answer: -6π but I'm not really sure if I...

*November 17, 2014 by Lily*

**Calculus**

Find the derivatives, dy/dx for the following functions. a. x^2y^4 = lnx + 3y b. y = ln(2x^2 + 1) c. y = ln(ãx) d. y = lnx/x e. y = x^2 lnx f. y ß log_2(3x)

*April 16, 2013 by Tima*

**Calculus**

Integrate [1/square root of(e^(2x)-1)]. I have to use u substitution. We are doing the integrals of inverse trig functions, but I cannot get it to work out!

*February 5, 2012 by Elaine*

**Please HELP! Calculus (Implicit functions)**

Find the inverse of the function y = (square root x) + 4x , then solve for its 1st order derivative.

*April 12, 2016 by Wawen*

**Algebra**

Use composition of functions to show that the functions f(x) = 5x + 7 and g(x)= 1/5x-7/5 are inverse functions. That is, carefully show that (fog)(x)= x and (gof)(x)= x.

*July 29, 2009 by Alicia*

**Inverse functions**

Solve for y to determine the inverse y=2-(1/2x)

*July 23, 2010 by Nada*

**Inverse Functions**

Given that g is the inverse function of f, and f(3)=4, and f'(3)=5, then g'(4)= ?

*June 5, 2012 by Ellen*

**calculus**

find the second-order partial derivatives of f(x,y)=x^3 + x^2y^2 + y^3 + x+y and show that the mixed partial derivatives fxy and fyx are equal

*March 7, 2012 by maggie*

**Math - Calculus 1**

Approximate using derivatives. (Must show work using derivatives!) Do not use a calculator: (1.1)^4 - (1.1)^2

*October 7, 2016 by James*

**Pre Calculus**

Inverse functions find the value If f(x)=1/x, find f^-1 (2)

*October 22, 2011 by Josh*

**End behavior models**

Thanks for the help with my previous problems Roger & Leo. It was really helpful. Now I want to know how to find the right and left end behavior models and horizontal tangents for the inverse functions, say y = tan inverse(x) I have to do this for all functions, but at least ...

*October 20, 2006 by Jen*

**Algebra Help ASAP PLEASE!**

((I forgot how to do find inverse functions and this is important)) Find the inverse function of g(x) = 2x + 4. A) g^(-1)(x) = 4x + 2 B) g^(-1)(x) = 2x + 1/2 C) g^(-1)(x) = 1/2x - 2 D) g^(-1)(x) = 2x - 4 I *think* it might be C but I'm not sure.

*March 16, 2017 by Tori*

**inverse functions**

1-3cos=sin squared You need to define the variables, such as x, y etc. If you are trying to solve 1 - 3 cos x = sin^2 x for whatever x is, then you are not talking about an inverse function.

*February 26, 2007 by fiza*

**calculus please help asap**

true or false questions: a)The derivatives of the reciprocal trigonometric functions can be found using the chain rule and their related base functions. b) A sinusoidal function can be differentiated only if the independent variable is measured in radians. c) There are an ...

*October 31, 2014 by Tina*

**Algebra**

How do you find the inverse of functions? for example how would you find the inverse of y= log8 x

*May 1, 2011 by Kenya*

**Calculus**

We're learning about different kinds of functions and I don't really understand the difference between rational and algebraic functions. I know that rational functions are functions that are a ratio of two polynomials, and algebraic functions are any functions that can be made...

*September 13, 2007 by Kelly*

**Trigonometry**

Having trouble with true/false questions in Trigonometry. They read as follows - True or False: For a trigonometric function, y=f(x), then x=F^-1(y). Explain your answer. True or False: For a one to one function, y=f(x), then x=f^-1(y). Explain your answer. True or False: For ...

*March 24, 2011 by Veronica*

**Trigonometry**

Having trouble with true/false questions in Trigonometry. They read as follows - True or False: For a trigonometric function, y=f(x), then x=F^-1(y). Explain your answer. True or False: For a one to one function, y=f(x), then x=f^-1(y). Explain your answer. True or False: For ...

*March 24, 2011 by Veronica*

**Calculus (Derivatives)**

What is the derivative of the this functon? g(x) = -500/x, x cannot equal 0. I know that in order to fnd the derivative I need to put the function into the equation for evaluating derivatives as limits. lim as h -> 0 (f(x+h) - f(x))/h I did this, but I am having ...

*November 1, 2011 by Mishaka*

**Algebra 2**

Are the functions f and g inverse functions if f(x)=5/3x+1 and g(x)=3(x-1)/5? I need all of the steps on how to determine this. I need this ASAP because this assignment is due tomorrow. Thanks

*May 25, 2011 by Brandon*

**math**

consider the functions f(x)=x^3-2 and g(x)=3 sqrt x+2: a. find f(g(x)) b. find g(f(x)) c. determine whether the functions f and g are inverse of each other. I have no clue where to even begin!

*March 23, 2013 by marie*

**calc**

find the derivatives of the given functions. g(t)=sqrt t(1+t)/t^2

*February 5, 2013 by Jake*

**convert derivatives of x,y,z, to r, Ɵ,z**

convert derivatives of x,y,z, to r, Ɵ,z with chain rule? I want provment rules of converting rectangular derivatives to cylindrical derivatives and and also cylindrical to spherical.I know the rules but I cant prove EQUATIONS.thx alot

*December 1, 2011 by parsa*

**math**

I studied derivatives before, but kind of forgot them all, is there a website that gives me an overview of derivatives. What is first and second derivatives, how to find it, all the derivative rules and so on... thank you

*October 9, 2008 by Sam*

**Algebra 2**

Ok, so I'm trying to find the inverse of each function. We're learning about Inverse Functions and Relations. The problem is f(x)=sqr.root of x/6 The sqr root is confusing me.

*September 17, 2012 by claire*

**algebra**

Can someone help with inverse relations and functions? is relation t a function? Is the inverse t a function? chart looks like: x 0 2 4 6 y -10 -1 4 8 If someone could please explain this problem

*December 10, 2012 by lee*

**Functions - math**

The function f is such that f(x) = a^2x^2 - ax + 3b for x<=(1/2a), where a and b are constants. 1) For the case where f(-2) = 4a^2 - b +8 and f(-3) = 7a^2 - b + 14, find the possible values of a and b. 2) For the case where a = 1 and b = -1, find an expression for inverse f...

*October 15, 2016 by Desperately seeking help*

**Calculus**

solve this equation on the given interval expressing the solution for x in terms of inverse trigonometric functions. 6(cosx)^2-cosx-5=0 on (pie/2, pie)

*October 10, 2011 by Josh*

**Pre-Calculus**

g(x)= x^2+7 Find the inverse of g(x) and state the domain and range for the inverse of g(x) using interval notation

*April 26, 2016 by Juniper*

**Calculus**

Does f(x)= 1 + cos(x), have an inverse or not, if so, what is the inverse? please explain.

*February 15, 2011 by Carrie*

**calculus**

Find the inverse of the following function. Find the domain, range, and asymptotes of each function. Graph both functions on the same coordinate plane. f(x)=3+e^4−x

*September 27, 2013 by Miriam*

**calculus (gr 12)**

Determine the velocity and acceleration as functions of time, t, for s(t) = 45t − 5t^2, where s(t) represents the distance as a function of time. (Hint: velocity and acceleration correspond to the first and second derivatives of the distance)

*April 16, 2013 by Alexandra*

**calculus (gr 12)**

Determine the velocity and acceleration as functions of time, t, for s(t) = 45t − 5t^2, where s(t) represents the distance as a function of time. (Hint: velocity and acceleration correspond to the first and second derivatives of the distance)

*April 17, 2013 by HELP MEE*

**Grade 12 Calculus**

Determine the velocity and acceleration as functions of time, t, for s(t) = 45t − 5t^2, where s(t) represents the distance as a function of time. (Hint: velocity and acceleration correspond to the first and second derivatives of the distance)

*April 15, 2013 by alex*

**pre calculus**

If f and g are inverse functions and the point (-3, 5) is on the graph of f, then the point ____ is on the graph of g

*October 10, 2011 by vedo*

**Calculus**

I have a two part question that pertains to a curve (r(x)) and its tangent line at x=3. We are given that at x=3, r(x)=8. In order to find the slope of the tangent line, we are given another point (on the tangent line): (3.2, 8.5). Therefore the slope of the tangent line at x=...

*March 31, 2009 by Lauren*

**Calculus**

If g(X) = 2+ln(x-5), find the inverse function, (g^(-1))(x) Solution: y = 2+ ln(x-5) e^y = 2 + x - 5 x = e^y + 3 y = e^x + 3 g^(-1) = y = e^x + 3 Is that right? I'm following an example - but don't really get it - how do I determine the domain and range - I know they flip when...

*September 3, 2016 by Linda*

**pre calculus**

Find the inverse of the following function. Find the domain, range, and asymptotes of each function. Graph both functions on the same coordinate plane. F(x)= ln(8-x) I am totally lost, somebody please help????

*April 24, 2013 by trish*

**calculus**

f(x)=sqrt(x-2) what is the inverse of f? I got inverse f(x)= x^2+2 however, you need to specify the domain of x. the answer key says when x=>0 can you please explain why? I thought it would be when x=>2 ?

*December 18, 2013 by Anonymous*

**calculus**

f(x)= 3x^7 +2x -9 If g(x)= f inverse of x and g(-4)= 1, what is g'(-4)? I know that f inverse is the same as 1/f'(x) but I'm not sure where to go from there.

*February 21, 2012 by k*

**pre calculus**

Find the inverse of the function below. Graph the function below and the inverse. Determine the domain, range and asymptotes of the function below and the inverse function. Please show all your work. f(x) = 2e^-x + 5 Just looking at this gives me a headache. HELP!

*December 20, 2011 by Michelle*

**math**

find the derivatives, dy/dx, for the following functions : y=(1+sin^2{2 exp (3x)})^5y please help me to solve this assignment. thank's

*August 20, 2012 by deel*

**Calculus**

Show that u(x, t) = f(x−ct)+g(x+ct), where c is a constant and f and g have continuous second derivatives, is a solution of the wave equation in one dimension, ie (∂t)^2 u = c^2 ∂x^2 u. Note that this solution to the wave equation consists of two functions ...

*September 30, 2015 by Margo*

**Algebra**

Given the functions f(x)=x+5/3 and g(x)=1/f^-1(x)+1, find the value of g(3). The first step would first be to find the inverse of x+1, the denominator of the fraction. I think the inverse would be 1-x. And now we have 1/1-x so we can just plu in 3. Right?

*November 4, 2014 by Trish Goal*

**Math - Derivatives**

How would one take the derivative of "f(x)^[g(x)]? Is there a formula I can follow to differentiate functions like that?

*January 28, 2009 by Anonymous*

**Functions**

What is the inverse of h(x)= (1/4x^2)+x ?

*October 5, 2012 by lola*

**Calculus/Derivatives**

In addition, can you walk me through how to get the derivatives for these 2 statements, too? a) y = x^5/3 - 5x^2/3 b) y = (the cubed root of the quantity) [(x^2 - 1)^2] Hi there. I need to find the first derivative of this statement. y=x(x+2)^3 I tried the chain rule, but I ...

*March 14, 2007 by Amy*

**advanced functions/precalculus**

1. Given f(x)=x^2 and g(x)=x+2, determine in standard form: a)g(f(x)) b)when f(g(x))=g(f(x)) for #1 would the answer for a be x^2+2? 2. Given the functions f(x)=5x+7 and g(x)=√x state the domain of g(x) and g(f(x)) 3. Why is point (a,a) a point on f-1(f(x)) if (a,b) is a...

*January 13, 2014 by Diane*

**Calculus**

Hello I need help with this excersise of derivative of a inverse function. The excersise says: If f(x+2)=x^3+1 and g(x)=f(arctg x), find the derivative of the inverse function of g(x) and then calculate (g^-1 (9))'[the derivative of the inverse function evaluated in 9] . I don...

*September 14, 2016 by Mary*

**Calculus grade 12**

a) determine the derivative of y = sin2x b) determine the derivative of y = 2SinxCosx c) shoe that derivatives in parts a) and b) are equal d) explain why derivatives in parts a) and be should be equal.

*April 12, 2012 by Julie*

**math**

Find the inverse of each of these functions a)f(x)=x/x+2 b)f(x)=2x/5-x c)f(x)=3x/2x+1

*October 17, 2013 by jason*

**Calculus, only two problems.**

If g(x) is the inverse of f(x), g(x)=f^-1(x), such that g(3)=5 and f'(5)=4 what is the value of g'(3)????? :O 2. If g(x)is the inverse of f(x), g(x)=f^-1(x), such that f(3)=15,f(6)=3,f'(3)=-8,and f'(6)=-2. What is the value of g'(3)???????? Calculus--

*March 23, 2010 by JakeT*

**math**

verify that f and g are inverse functions. f(x) = 5x^2 x>(or equal too)0 g(x)= (x+2/5)^1/2

*January 26, 2011 by Amanda*

**Math**

If f and g are inverse functions, f (7) =10 and f (10) = −1 , find g(10).

*October 12, 2011 by Caprice*

**Math**

Which of the following functions has an inverse that is not a function? a. (1,1),(1,2),(3,4) b. (1,2),(1,3),(4,3) c. (1,4),(4,5),(5,6) d. (0,0),(1,1),(2,2)

*November 17, 2015 by Kaai97*

**Math**

Which of the following functions is the inverse of the function {(1,2),(3,4),(6,8)}? a. {(6,8),(3,4),(1,2)} b. {(2,1),(4,3),(6,8)} c. {(2,1),(4,3),(8,6)} d. {(2,1),(3,4),(8,6)}***

*November 17, 2015 by Kaai97*

**precal**

Which of the following functions is the inverse of the function {(1,2),(3,4),(6,8)}? a. {(6,8),(3,4),(1,2)} b. {(2,1),(4,3),(6,8)} c. {(2,1),(4,3),(8,6)} d. {(2,1),(3,4),(8,6)}

*March 27, 2017 by Emily*

**Calculus**

show that the curves r=asin(è) and r=acos(è) intersect at right angles. can you show that the derivatives for each are the negative reciprocal of each other? That is the key. i need more info..i know how to find the derivative...but how will that prove my question. Do I need...

*April 5, 2007 by Amy*

**pre-cal**

How do you work inverse functions alebraically?

*September 20, 2007 by chris*

**Maths Calculus Derivatives**

Find the first derivative for the following functions 1) f(x) = sin(cos^2x) cos(sin^3x) 2) f(x) = ( tan 2x - tan x ) / ( 1 + tan x tan 2x ) 3) f(x) = sin { tan ( sqrt x^3 + 6 ) } 4) f(x) = {sec^2(100x) - tan^2(100x)} / x

*October 22, 2011 by Yousef*

**calculus**

derivatives. f(x)=(1/-7x^12) f'(2)=? f'(-1)=?

*January 18, 2008 by mike*

**Derivatives ~ Calculus**

If dy/dx = (1 + x)/(xy), x>0, and y=-4 when x=1, then when x=3, y= what?

*June 5, 2012 by Hannah*

**calculus**

a)find the first partial derivatives of f(x y)= x √1+y^2 b)find the first partial derivatives of f(x,y)= e^x ln y at the point (0,e)

*March 11, 2012 by maria*

**algebra**

Which of the following functions has an inverse that is not a function? y=x y=2x+1 y=x to the second power

*May 25, 2011 by Loren*

**MATH**

Two functions g and h are defined as : g:x--> 2x+3/x-4 h:x --> 1/x Write expressions for : a) hg(x) b) g inverse 1(x)

*September 7, 2011 by Nelly*

**MATH**

Two functions g and h are defined as : g:x--> 2x+3/x-4 h:x --> 1/x Write expressions for : a) hg(x) b) g inverse 1(x)

*September 7, 2011 by Nelly*

**MATH**

Two functions g and h are defined as : g:x--> 2x+3/x-4 h:x --> 1/x Write expressions for : a) hg(x) b) g inverse 1(x)

*September 7, 2011 by Nelly*

**MATH HELP**

Two functions g and h are defined as : g:x--> 2x+3/x-4 h:x --> 1/x Write expressions for : a) hg(x) b) g inverse 1(x)

*September 8, 2011 by Nelly*

**College Algebra**

verify that the functions of f and g are inverse of each other by showing that f(g(x))=x and g(f(x))=x; f(x)=In(x-1),g(x)=1+e^x

*January 1, 2012 by Jennifer*

**Calculus**

Compute the derivatives of : f(x)= x^7 + 7^x+ 7^7

*November 22, 2010 by JJ*

**Calculus-derivatives**

Determine h'(x) for h(x)= [x/(1-x)]^2

*February 20, 2012 by Jessi*

**calculus**

Anti-Derivatives 2x^6-x^3/x^2

*December 11, 2015 by Jason*

**Calculus, check my answers, please! 3**

Did I get these practice questions right? 1. Suppose that f is an even function whose domain is the set of all real numbers. Then which of the following can we claim to be true? ***The function f has an inverse f –1 that is even. The function f has an inverse f –1, but we ...

*October 2, 2013 by Samantha*

**Pre-Calculus**

Operations with Functions write the function below as either a sum/difference/product/quotient of 2 r more functions a. h(x) = x^2+3x+9 How Would I do this? My teacher just did this f(x) = x^2 g(x) 3x+9 ^I don't really understand h(x)=(x+5)(x-3) how would I do this one? If h(x...

*September 26, 2012 by Shreya*

**Calculus**

Math questions, please help me? :(? Find the composite functions f o g and g o f for the given functions. f(x) = 10^x and g(x) = log x State the domain and range for each: f(x) = 4x + 1 and g(x) = x^2 f(x) = sin x and g(x) = x^2 - x + 1 f(x) = 10^x and g(x) = log x If f = {(-2...

*September 2, 2013 by Britt*

**Functions - math**

The function f is such that f(x) = 2x + 3 for x ≥ 0. The function g is such that g(x)= ax^2 + b for x ≤ q, where a, b and q are constants. The function fg is such that fg(x)= 6x^2 − 21 for x ≤ q. i)Find the values of a and b ii) Find the greatest possible value of q...

*December 10, 2016 by Desperately seeking help*

**Pre-Calculus/Calculus**

I am too embarassed to ask this Calculus (really pre-calculus) question in tutoring, because I know I should know. Is the inverse of f(x)=3x-1 actually f(x)=1/3x+1? How do I find it? What if it asks the same equation replaced with f to the -1 power (x)? I think I know how the ...

*July 1, 2008 by Molly*

**Calculus**

Okay so I have a question on my assignment that says: You are given that tan(y) = x. Find sin(y)^2. Express your answer in terms of x. I know its derivatives, and I've tried taking the derivatives of both etc, and got them both to come out as cos(y)^2, which I know can be ...

*October 21, 2006 by Tracy*