7 Fig. 7 shows the curve \(y = \mathrm { f } ( x )\), where \(\mathrm { f } ( x ) = 1 + 2 \arctan x , x \in \mathbb { R }\). The scales on the \(x\) - and \(y\)-axes are the same.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{9857ad89-b315-4cd6-8d8d-26a509ca52a8-3_859_849_386_648}
\captionsetup{labelformat=empty}
\caption{Fig. 7}
\end{figure}
- Find the range of f , giving your answer in terms of \(\pi\).
- Find \(\mathrm { f } ^ { - 1 } ( x )\), and add a sketch of the curve \(y = \mathrm { f } ^ { - 1 } ( x )\) to the copy of Fig. 7.
Section B (36 Marks)