5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{bcb0c693-66ae-4b97-99f8-b10fb9396886-07_721_1217_237_397}
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\caption{Figure 2}
\end{figure}
Figure 2 shows a sketch of part of the curve with equation \(y = \mathrm { f } ( x ) , x \in \mathbb { R }\).
The curve meets the coordinate axes at the points \(A ( 0,1 - k )\) and \(B \left( \frac { 1 } { 2 } \ln k , 0 \right)\), where \(k\) is a constant and \(k > 1\), as shown in Figure 2.
On separate diagrams, sketch the curve with equation
- \(y = | f ( x ) |\),
- \(y = \mathrm { f } ^ { - 1 } ( x )\).
Show on each sketch the coordinates, in terms of \(k\), of each point at which the curve meets or cuts the axes.
Given that \(\mathrm { f } ( x ) = \mathrm { e } ^ { 2 x } - k\),
- state the range of f ,
- find \(\mathrm { f } ^ { - 1 } ( x )\),
- write down the domain of \(\mathrm { f } ^ { - 1 }\).