CAIE P1 2022 June — Question 6

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2022
SessionJune
TopicComposite & Inverse Functions

6 The function \(f\) is defined as follows: $$\mathrm { f } ( x ) = \frac { x ^ { 2 } - 4 } { x ^ { 2 } + 4 } \quad \text { for } x > 2$$
  1. Find an expression for \(\mathrm { f } ^ { - 1 } ( x )\).
  2. Show that \(1 - \frac { 8 } { x ^ { 2 } + 4 }\) can be expressed as \(\frac { x ^ { 2 } - 4 } { x ^ { 2 } + 4 }\) and hence state the range of f .
  3. Explain why the composite function ff cannot be formed.