9 Functions f and g are defined by
$$\begin{array} { l l }
\mathrm { f } : x \mapsto 2 x + 3 & \text { for } x \leqslant 0
\mathrm {~g} : x \mapsto x ^ { 2 } - 6 x & \text { for } x \leqslant 3
\end{array}$$
- Express \(\mathrm { f } ^ { - 1 } ( x )\) in terms of \(x\) and solve the equation \(\mathrm { f } ( x ) = \mathrm { f } ^ { - 1 } ( x )\).
- On the same diagram sketch the graphs of \(y = \mathrm { f } ( x )\) and \(y = \mathrm { f } ^ { - 1 } ( x )\), showing the coordinates of their point of intersection and the relationship between the graphs.
- Find the set of values of \(x\) which satisfy \(\operatorname { gf } ( x ) \leqslant 16\).