Question

Let f(x) = (2/3)x^3 - 2x + 1 with a restricted domain of [1,infinity]. What is the value of (f-1)'(x) when x = 13?

Answer 1

since x = f^-1(y)
and dx/dy = 1/y'
f' = 2x^2-2

(f^-1)'(13) = 1/f'(13) = 1/(2*169-2) = 1/336

Answer 2

Okay, I see the logic of this now, but I have another problem. This is for a multichoice worksheet, and the four choices are 1/13, 13, 3, & 1/16. Which one is the correct choice?

Answer 3

Well, that's a rum 'un. You can see that when x=13, the curve for f(x) is extremely steep.

However, I see a possible solution. If there is a typo in the problem, ad you want (f^-1)'(3), then that is in fact 1/16