10 The functions \(f\) and \(g\) are defined by
$$\begin{array} { l l }
\mathrm { f } : x \mapsto 3 x + 2 , & x \in \mathbb { R } ,
\mathrm {~g} : x \mapsto \frac { 6 } { 2 x + 3 } , & x \in \mathbb { R } , x \neq - 1.5 .
\end{array}$$
- Find the value of \(x\) for which \(\operatorname { fg } ( x ) = 3\).
- Sketch, in a single diagram, the graphs of \(y = \mathrm { f } ( x )\) and \(y = \mathrm { f } ^ { - 1 } ( x )\), making clear the relationship between the two graphs.
- Express each of \(\mathrm { f } ^ { - 1 } ( x )\) and \(\mathrm { g } ^ { - 1 } ( x )\) in terms of \(x\), and solve the equation \(\mathrm { f } ^ { - 1 } ( x ) = \mathrm { g } ^ { - 1 } ( x )\).