9 Functions f and g are defined as follows:
$$\begin{aligned}
& \mathrm { f } ( x ) = ( x - 2 ) ^ { 2 } - 4 \text { for } x \geqslant 2 ,
& \mathrm {~g} ( x ) = a x + 2 \text { for } x \in \mathbb { R } ,
\end{aligned}$$
where \(a\) is a constant.
- State the range of f.
- Find \(\mathrm { f } ^ { - 1 } ( x )\).
- Given that \(a = - \frac { 5 } { 3 }\), solve the equation \(\mathrm { f } ( x ) = \mathrm { g } ( x )\).
- Given instead that \(\operatorname { ggf } ^ { - 1 } ( 12 ) = 62\), find the possible values of \(a\).