4.A curve $C$ has equation $y = \mathrm { f } ( x )$ where $x \in \mathbb { R }$ and f is a one-one function.
\begin{enumerate}[label=(\alph*)]
\item 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 $y = \mathrm { g } ( x )$ .
\item Explain why $\mathrm { g } ^ { - 1 } ( x ) = - \mathrm { f } ( - x )$ .

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{2a7c2530-a93c-4a26-bc37-c20c0f40c8f2-3_793_979_819_633}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}

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 $B$ .
\item Write down the value of $p$ and the value of $q$ .
\item 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),
\item find the function g .
\item Solve $\mathrm { g } ^ { - 1 } \mathrm { f } ( x ) = x$
\end{enumerate}

\hfill \mbox{\textit{Edexcel AEA 2018 Q4 [13]}}