CAIE P1 2017 November — Question 6

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2017
SessionNovember
TopicComposite & Inverse Functions

6 The functions f and g are defined by $$\begin{aligned} & \mathrm { f } ( x ) = \frac { 2 } { x ^ { 2 } - 1 } \text { for } x < - 1
& \mathrm {~g} ( x ) = x ^ { 2 } + 1 \text { for } x > 0 \end{aligned}$$
  1. Find an expression for \(\mathrm { f } ^ { - 1 } ( x )\).
  2. Solve the equation \(\operatorname { gf } ( x ) = 5\).