CAIE P1 2010 November — Question 7

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2010
SessionNovember
TopicComposite & Inverse Functions

7 A function f is defined by f : \(x \mapsto 3 - 2 \tan \left( \frac { 1 } { 2 } x \right)\) for \(0 \leqslant x < \pi\).
  1. State the range of f .
  2. State the exact value of \(\mathrm { f } \left( \frac { 2 } { 3 } \pi \right)\).
  3. Sketch the graph of \(y = \mathrm { f } ( x )\).
  4. Obtain an expression, in terms of \(x\), for \(\mathrm { f } ^ { - 1 } ( x )\).