4. The function \(f\) is defined by
$$\mathrm { f } : x \mapsto 4 - \ln ( x + 2 ) , \quad x \in \mathbb { R } , x \geqslant - 1$$
- Find \(\mathrm { f } ^ { - 1 } ( x )\).
- Find the domain of \(\mathrm { f } ^ { - 1 }\).
The function \(g\) is defined by
$$\mathrm { g } : x \mapsto \mathrm { e } ^ { x ^ { 2 } } - 2 , \quad x \in \mathbb { R }$$
- Find \(\mathrm { fg } ( x )\), giving your answer in its simplest form.
- Find the range of fg.