Question

(a) Express the formula for the derivative of an inverse function f^-1(x) of a function f(x)
(b) Let f(x) = x^3+x+1. Prove that f^-1(x) exists
(c) Find f^-1(3). (Note f(1)=3)

Answer 1

There is a formula for finding inverse derivatives, it is as follows: \[y' = \frac{ 1 }{ f'(f^{-1}(x)) }\]