The functions $f$ and $g$ are defined by

$f(x)=e^{2 x}-4, \quad x \in \mathbb{R}, $
$g(x)=x+2, \quad x \in \mathbb{R} .$

(i) Find $\mathrm{f}^{-1}(x)$ and state its domain.

[3]

(ii) Find the exact solution of $\operatorname{fg}(x)=5$, giving your answer in its simplest form.

[3]