Given the function

$\displaystyle f(x) = 5x^3 + 4x - 4$

Let g be the inverse function of f. i.e. g(x)=f−1(x).

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- Jan 20th 2010, 10:39 AMLolcatsFinding the Inverse Function
Given the function

$\displaystyle f(x) = 5x^3 + 4x - 4$

Let g be the inverse function of f. i.e. g(x)=f−1(x). - Jan 20th 2010, 10:57 AMCalculus26
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 - Jan 20th 2010, 11:06 AMLolcats
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)

- Jan 20th 2010, 11:12 AMCalculus26
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 - Jan 20th 2010, 11:22 AMLolcats
Thanks I was really confused how to go about it.

- Jan 20th 2010, 11:31 AMbigwave