6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{3db6c0d8-2c8a-47a2-8c98-13fa191320d0-3_727_1006_244_356}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows the curve with equation \(y = \mathrm { f } ( x )\). The curve crosses the axes at \(( p , 0 )\) and \(( 0 , q )\) and the lines \(x = 1\) and \(y = 2\) are asymptotes of the curve.
- Showing the coordinates of any points of intersection with the axes and the equations of any asymptotes, sketch on separate diagrams the graphs of
- \(y = | \mathrm { f } ( x ) |\),
- \(y = 2 \mathrm { f } ( x + 1 )\).
Given also that
$$\mathrm { f } ( x ) \equiv \frac { 2 x - 1 } { x - 1 } , \quad x \in \mathbb { R } , \quad x \neq 1$$
- find the values of \(p\) and \(q\),
- find an expression for \(\mathrm { f } ^ { - 1 } ( x )\).