10 Functions \(f\) and \(g\) are defined by
$$\begin{aligned}
& \mathrm { f } : x \mapsto 2 x - 5 , \quad x \in \mathbb { R } ,
& \mathrm {~g} : x \mapsto \frac { 4 } { 2 - x } , \quad x \in \mathbb { R } , \quad x \neq 2 .
\end{aligned}$$
- Find the value of \(x\) for which \(\mathrm { fg } ( x ) = 7\).
- Express each of \(\mathrm { f } ^ { - 1 } ( x )\) and \(\mathrm { g } ^ { - 1 } ( x )\) in terms of \(x\).
- Show that the equation \(\mathrm { f } ^ { - 1 } ( x ) = \mathrm { g } ^ { - 1 } ( x )\) has no real roots.
- Sketch, on a single diagram, the graphs of \(y = \mathrm { f } ( x )\) and \(y = \mathrm { f } ^ { - 1 } ( x )\), making clear the relationship between these two graphs.