9 Functions f and g are defined for \(x \in \mathbb { R }\) by
$$\begin{aligned}
& \mathrm { f } : x \mapsto \frac { 1 } { 2 } x - 2
& \mathrm {~g} : x \mapsto 4 + x - \frac { 1 } { 2 } x ^ { 2 }
\end{aligned}$$
- Find the points of intersection of the graphs of \(y = \mathrm { f } ( x )\) and \(y = \mathrm { g } ( x )\).
- Find the set of values of \(x\) for which \(\mathrm { f } ( x ) > \mathrm { g } ( x )\).
- Find an expression for \(\mathrm { fg } ( x )\) and deduce the range of fg .
The function h is defined by \(\mathrm { h } : x \mapsto 4 + x - \frac { 1 } { 2 } x ^ { 2 }\) for \(x \geqslant k\). - Find the smallest value of \(k\) for which h has an inverse.