Question

If f(x) = x^3-x-6 for all real numbers x, and if g is the inverse function of f, then f'(g(0))g'(0)=

Answer 1

\[f(g(x)) = x\]
\[\implies \frac{d}{dx} f(g(x)) = \frac{d}{dx}x\]
\[\implies f'(g(x)) * g'(x) = 1, \forall x \in R\]

Answer 2

\[\implies f'(g(0))g'(0) = 1\]