CAIE P1 2019 June — Question 9

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2019
SessionJune
TopicComposite & Inverse Functions

9 The function f is defined by \(\mathrm { f } ( x ) = 2 - 3 \cos x\) for \(0 \leqslant x \leqslant 2 \pi\).
  1. State the range of f .
  2. Sketch the graph of \(y = \mathrm { f } ( x )\). The function g is defined by \(\mathrm { g } ( x ) = 2 - 3 \cos x\) for \(0 \leqslant x \leqslant p\), where \(p\) is a constant.
  3. State the largest value of \(p\) for which g has an inverse.
  4. For this value of \(p\), find an expression for \(\mathrm { g } ^ { - 1 } ( x )\).