CAIE P1 2016 November — Question 8

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2016
SessionNovember
TopicComposite & Inverse Functions

8 The functions \(f\) and \(g\) are defined by $$\begin{aligned} & \mathrm { f } ( x ) = \frac { 4 } { x } - 2 \quad \text { for } x > 0
& \mathrm {~g} ( x ) = \frac { 4 } { 5 x + 2 } \quad \text { for } x \geqslant 0 \end{aligned}$$
  1. Find and simplify an expression for \(\mathrm { fg } ( x )\) and state the range of fg.
  2. Find an expression for \(\mathrm { g } ^ { - 1 } ( x )\) and find the domain of \(\mathrm { g } ^ { - 1 }\).