# Finding the Inverse Function

• Jan 20th 2010, 10:39 AM
Lolcats
Finding 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 AM
Calculus26
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 AM
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)
• Jan 20th 2010, 11:12 AM
Calculus26
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 AM
Lolcats
Thanks I was really confused how to go about it.
• Jan 20th 2010, 11:31 AM
bigwave
Quote:

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)