10 Functions \(f\) and \(g\) are defined by
$$\begin{aligned}
& \mathrm { f } : x \mapsto 2 x + 1 , \quad x \in \mathbb { R } , \quad x > 0
& \mathrm {~g} : x \mapsto \frac { 2 x - 1 } { x + 3 } , \quad x \in \mathbb { R } , \quad x \neq - 3
\end{aligned}$$
- Solve the equation \(\operatorname { gf } ( x ) = x\).
- Express \(\mathrm { f } ^ { - 1 } ( x )\) and \(\mathrm { g } ^ { - 1 } ( x )\) in terms of \(x\).
- Show that the equation \(\mathrm { g } ^ { - 1 } ( x ) = x\) has no solutions.
- Sketch in a single diagram the graphs of \(y = \mathrm { f } ( x )\) and \(y = \mathrm { f } ^ { - 1 } ( x )\), making clear the relationship between the graphs.