CAIE P1 2012 November — Question 6

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2012
SessionNovember
TopicComposite & Inverse Functions

6 The functions f and g are defined for \(- \frac { 1 } { 2 } \pi \leqslant x \leqslant \frac { 1 } { 2 } \pi\) by $$\begin{aligned} & f ( x ) = \frac { 1 } { 2 } x + \frac { 1 } { 6 } \pi
& g ( x ) = \cos x \end{aligned}$$ Solve the following equations for \(- \frac { 1 } { 2 } \pi \leqslant x \leqslant \frac { 1 } { 2 } \pi\).
  1. \(\operatorname { gf } ( x ) = 1\), giving your answer in terms of \(\pi\).
  2. \(\operatorname { fg } ( x ) = 1\), giving your answers correct to 2 decimal places.