please help

Question

If f is a one-to-one function with f(1)=−5 and f⁡⁡′(1)=2, what is the value of (f^−1)′(−5).

Answer 1

If f and g are inverses then 

g'(X) = 1/[f'(g(X))]

you can derive this using the fact 

f(g(X)) = X and take derivative with chain rule.

 

thus g'(-5) = 1/f'(g(-5)) = 1/f'(1) = 1/2

 

note g(-5) = 1 since g is inverse of f and we are given f(1) = -5.