Integration with inverse functions

[Shannabel]

Homework Statement

let f(x)=(4t^3+4t)dt(between 2 and x)
if g(x) = f^(-1)(x), then g'(0)=?

Homework Equations

The Attempt at a Solution

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

 

[Bohrok]

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

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

 

[Shannabel]

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

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

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...

 

[Bohrok]

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...

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)

 

[Shannabel]

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)

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

 

[Bohrok]

at the beginning you started with f(f^(-1)(x))=x
... where did that come from?

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" has a pretty good article with examples.

 

[Shannabel]

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" has a pretty good article with examples.

thanks!