CAIE P1 2005 June — Question 7

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2005
SessionJune
TopicComposite & Inverse Functions

7 A function f is defined by f : \(x \mapsto 3 - 2 \sin x\), for \(0 ^ { \circ } \leqslant x \leqslant 360 ^ { \circ }\).
  1. Find the range of f .
  2. Sketch the graph of \(y = \mathrm { f } ( x )\). A function g is defined by \(\mathrm { g } : x \mapsto 3 - 2 \sin x\), for \(0 ^ { \circ } \leqslant x \leqslant A ^ { \circ }\), where \(A\) is a constant.
  3. State the largest value of \(A\) for which g has an inverse.
  4. When \(A\) has this value, obtain an expression, in terms of \(x\), for \(\mathrm { g } ^ { - 1 } ( x )\).