OCR MEI C3 — Question 1

Exam BoardOCR MEI
ModuleC3 (Core Mathematics 3)
TopicComposite & Inverse Functions

1 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]{7825ba53-67eb-4050-a671-85e37a30150a-1_420_616_538_759} \captionsetup{labelformat=empty} \caption{Fig. 4}
\end{figure}
  1. Find \(a\) and \(b\).
  2. Find \(\mathrm { f } ^ { - 1 } ( x )\), and state its domain and range.