# Homework Help: Integration with inverse functions

1. Aug 12, 2011

### Shannabel

1. The problem statement, all variables and given/known data
let f(x)=(4t^3+4t)dt(between 2 and x)
if g(x) = f^(-1)(x), then g'(0)=?

2. Relevant equations

3. The attempt at a solution
f'(x) = 4x^3+4x
annd i already don't know where to go from here.. help?

2. Aug 12, 2011

### Bohrok

There's a formula for the derivative of inverses
http://en.wikipedia.org/wiki/Inverse_functions_and_differentiation" [Broken]

If you start with f(f-1(x)) = x, differentiate both sides and rearrange and you'll get something like

Last edited by a moderator: May 5, 2017
3. Aug 12, 2011

### Shannabel

so
[f^(-1)(0)]' = 1/[f'(f^(-1)(0))]
but where do i go from here?
because i don't know what f^(-1)(0) is...

Last edited by a moderator: May 5, 2017
4. Aug 12, 2011

### Bohrok

If f(b) = 0, then taking the inverse of both sides gives you f-1(0) = b. Then you apply this to the original function you were given to find f-1(0)

5. Aug 12, 2011

### Shannabel

got it :)
one other thing, at the beginning you started with f(f^(-1)(x))=x
... where did that come from?

6. Aug 12, 2011

### Bohrok

That's the purpose of the inverse functions: the compositions of inverse functions return the input x, f(f-1(x)) = f-1(f(x)) = x. http://en.wikipedia.org/wiki/Inverse_function" [Broken] has a pretty good article with examples.

Last edited by a moderator: May 5, 2017
7. Aug 12, 2011

### Shannabel

thanks!

Last edited by a moderator: May 5, 2017