10 The functions \(f\) and \(g\) are defined as follows:
$$\begin{array} { l l }
\mathrm { f } : x \mapsto x ^ { 2 } - 2 x , & x \in \mathbb { R } ,
\mathrm {~g} : x \mapsto 2 x + 3 , & x \in \mathbb { R } .
\end{array}$$
- Find the set of values of \(x\) for which \(\mathrm { f } ( x ) > 15\).
- Find the range of f and state, with a reason, whether f has an inverse.
- Show that the equation \(\operatorname { gf } ( x ) = 0\) has no real solutions.
- Sketch, in a single diagram, the graphs of \(y = \mathrm { g } ( x )\) and \(y = \mathrm { g } ^ { - 1 } ( x )\), making clear the relationship between the graphs.