The function f(x) has an inverse function, g(x). Find g'(5).
[itex]f(x) = x^5 + 2x^2 + 2x[/itex]
The Attempt at a Solution
I don't see how I can possibly find the inverse of this function. So I opted to use the derivative rule for inverses.
[itex] f'(x) = 5x^4 + 4x + 2[/itex]
[itex] 5 = x^5 + 2x^2 + 2x[/itex]
This doesn't help me either. I need to solve for x in the second equation and substitute that x in the derivative. In essence, I can't find x of f(x), and without that I can't find the value of f'(x), which is the reciprocal of g'(x).
Any help would be appreciated!