derivative of a inverse function

Question

Let $f(x) = x^3 + 3x^2 - 33x - 33$ for $x>0$ and $g$ be its inverse such that $kg'(2)=1$, then the value of $k$ is. Answer for the following is $72$. I approach this question by $f\circ g=x$ but I got struck at part $f'\bigl(g(2)\bigr)=k$. Also I would like to know that does $g(x)$ will also be a cubic function as $f(x)$. If so any proof/counter- example for this.