6 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]{0ee3d87a-0d9e-4fa5-b8f5-8b28489e65b5-3_378_725_367_669}
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\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.