- The functions \(f\) and \(g\) are defined by
$$\begin{aligned}
& \mathrm { f } : x \rightarrow 7 x - 1 , \quad x \in \mathbb { R }
& \mathrm {~g} : x \rightarrow \frac { 4 } { x - 2 } , \quad x \neq 2 , x \in \mathbb { R }
\end{aligned}$$
- Solve the equation \(\operatorname { fg } ( x ) = x\)
- Hence, or otherwise, find the largest value of \(a\) such that \(\mathrm { g } ( a ) = \mathrm { f } ^ { - 1 } ( a )\)