The problem provided in the image is as follows:

Given:

$f(x) = \ln(x - 1) + \ln 4$, for $x > 1$.

Tasks:

a) Find $f'(x)$.
Let $g(x) = e^{f(x)}$ for $x \in \mathbb{R}$.

b) Find $g(f^{-1}(x))$, giving your answer in the form $ax + b$, where ( a, b \in \mathbb{Z}