Let f be a differentiable function such that f(3)=15, f(6)=3, f ' (3)= -8, and f ' (6)= -2. The function g is differentiable and g(x)= f inverse (x) for all x. What is the value of g '(3)

Question

A: -1/2

B: -1/8

C: 1/6

D: 1/3

E: Value cannot be determined

I am trying to quiz myself but i cannot solve this problem, any help would be amazing!

Answer 1

f(6) = 3, so f^-1(3) = 6

g'(3) = [f^-1(3)]' = 1 / [f'(6)] = 1 / (-2) = -1/2