## anonymous 5 years ago 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)=

1. anonymous

2. anonymous

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

3. anonymous

$\implies f'(g(0))g'(0) = 1$