4 Fig. 4 shows the curve \(y = \mathrm { f } ( x )\), where
$$f ( x ) = a + \cos b x , 0 \leqslant x \leqslant 2 \pi ,$$
and \(a\) and \(b\) are positive constants. The curve has stationary points at \(( 0,3 )\) and \(( 2 \pi , 1 )\).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c1a06289-d9e9-4f6b-ab58-70db1a4748ef-2_424_620_922_719}
\captionsetup{labelformat=empty}
\caption{Fig. 4}
\end{figure}
- Find \(a\) and \(b\).
- Find \(\mathrm { f } ^ { - 1 } ( x )\), and state its domain and range.