CAIE P1 2014 November — Question 11

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2014
SessionNovember
TopicComposite & Inverse Functions

11 The function f : \(x \mapsto 6 - 4 \cos \left( \frac { 1 } { 2 } x \right)\) is defined for \(0 \leqslant x \leqslant 2 \pi\).
  1. Find the exact value of \(x\) for which \(\mathrm { f } ( x ) = 4\).
  2. State the range of f.
  3. Sketch the graph of \(y = \mathrm { f } ( x )\).
  4. Find an expression for \(\mathrm { f } ^ { - 1 } ( x )\).