4．A curve \(C\) has equation \(y = \mathrm { f } ( x )\) where \(x \in \mathbb { R }\) and f is a one－one function．
（a）Describe a single transformation that transforms \(C\) to the curve with equation \(y = - \mathrm { f } ( - x )\) ．
The curve \(C\) is reflected in the line with equation \(y = - x\) to give the curve \(V\) ． The equation of \(V\) is \(y = \mathrm { g } ( x )\) ．
（b）Explain why \(\mathrm { g } ^ { - 1 } ( x ) = - \mathrm { f } ( - x )\) ．
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{2a7c2530-a93c-4a26-bc37-c20c0f40c8f2-3_793_979_819_633}
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\caption{Figure 1}
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Figure 1 shows a sketch of the curve \(C\) with equation \(y = \mathrm { f } ( x )\) where
$$\mathrm { f } ( x ) = \frac { 3 ( x - 1 ) } { x - 2 } \quad x \in \mathbb { R } , x \neq 2$$
The curve has asymptotes with equations \(x = p\) and \(y = q\) and \(C\) crosses the \(x\)－axis at the point \(A\) and the \(y\)－axis at the point \(B\) ．
（c）Write down the value of \(p\) and the value of \(q\) ．
（d）Write down the coordinates of the point \(A\) and the coordinates of the point \(B\) ．
Given the definition of \(\mathrm { g } ( x )\) in part（b），
（e）find the function g ．
（f）Solve \(\mathrm { g } ^ { - 1 } \mathrm { f } ( x ) = x\)