3 The function \(\mathrm { f } ( x )\) is defined by \(\mathrm { f } ( x ) = 1 - 2 \sin x\) for \(- \frac { 1 } { 2 } \pi \leqslant x \leqslant \frac { 1 } { 2 } \pi\). Fig. 3 shows the curve \(y = \mathrm { f } ( x )\).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{7825ba53-67eb-4050-a671-85e37a30150a-3_743_818_414_644}
\captionsetup{labelformat=empty}
\caption{Fig. 3}
\end{figure}
- Write down the range of the function \(\mathrm { f } ( x )\).
- Find the inverse function \(\mathrm { f } ^ { - 1 } ( x )\).
- Find \(\mathrm { f } ^ { \prime } ( 0 )\). Hence write down the gradient of \(y = \mathrm { f } ^ { - 1 } ( x )\) at the point \(( 1,0 )\).