7 Functions f and g are defined as follows:
$$\begin{aligned}
& \mathrm { f } : x \mapsto x ^ { 2 } + 2 x + 3 \text { for } x \leqslant - 1 ,
& \mathrm {~g} : x \mapsto 2 x + 1 \text { for } x \geqslant - 1 .
\end{aligned}$$
- Express \(\mathrm { f } ( x )\) in the form \(( x + a ) ^ { 2 } + b\) and state the range of f .
- Find an expression for \(\mathrm { f } ^ { - 1 } ( x )\).
- Solve the equation \(\operatorname { gf } ( x ) = 13\).