2 Fig. 6 shows the curve \(y = \mathrm { f } ( x )\), where \(\mathrm { f } ( x ) = \frac { 1 } { 2 } \arctan x\).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{6555136d-0444-41f6-9063-21960352089d-2_388_727_434_701}
\captionsetup{labelformat=empty}
\caption{Fig. 6}
\end{figure}
- Find the range of the function \(\mathrm { f } ( x )\), giving your answer in terms of \(\pi\).
- Find the inverse function \(\mathrm { f } ^ { - 1 } ( x )\). Find the gradient of the curve \(y = \mathrm { f } ^ { - 1 } ( x )\) at the origin.
- Hence write down the gradient of \(y = \frac { 1 } { 2 } \arctan x\) at the origin.