8 Functions f and g are defined by
$$\begin{aligned}
& \mathrm { f } ( x ) = ( x + a ) ^ { 2 } - a \text { for } x \leqslant - a ,
& \mathrm {~g} ( x ) = 2 x - 1 \text { for } x \in \mathbb { R } ,
\end{aligned}$$
where \(a\) is a positive constant.
- Find an expression for \(\mathrm { f } ^ { - 1 } ( x )\).
- State the domain of the function \(f ^ { - 1 }\).
- State the range of the function \(f ^ { - 1 }\).
- Given that \(a = \frac { 7 } { 2 }\), solve the equation \(\mathrm { gf } ( x ) = 0\).