# Thread: Finding the Inverse Function

1. ## Finding the Inverse Function

Given the function
$f(x) = 5x^3 + 4x - 4$
Let g be the inverse function of f. i.e. g(x)=f−1(x).

2. what is the entire pblm? In general it is very difficulat to solve a cubic equation see Cubic function - Wikipedia, the free encyclopedia

I would be willing to bet to solve you're given pblm we may not need

to solve for f^(-1)(x) in general

3. its asking me to find the inverse of f(x) and then enter f(5) then do the same but with the derivative so f'(5)

4. If you want f ^(-1)(5)

f(x) = 5x^3 + 4x -4

note f(1) =5 so f^(-1)(5) = 1

For the derivative [f^(-1)] ' (5) use the theorem on the derivative of the inverse:

if f(a) = c

Then [f^(-1)] ' (c) = 1/f '(a)

In terms of g : g ' (c) =1/f '(a)

In particular [f^(-1)] ' (5) = 1/f '(1) = 1/19

5. Thanks I was really confused how to go about it.

6. Originally Posted by Lolcats
its asking me to find the inverse of f(x) and then enter f(5) then do the same but with the derivative so f'(5)