2. The function \(f\) is defined by
$$\mathrm { f } : x \mapsto 2 x , \quad x \in \mathbb { R }$$
- Find \(\mathrm { f } ^ { - 1 } ( x )\) and state the domain of \(\mathrm { f } ^ { - 1 }\).
The function g is defined by
$$\mathrm { g } : x \mapsto 3 x ^ { 2 } + 2 , \quad x \in \mathbb { R }$$
- Find \(\mathrm { gf } ^ { - 1 } ( x )\).
- State the range of \(\mathrm { gf } ^ { - 1 } ( x )\).