CAIE P1 2021 June — Question 8

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2021
SessionJune
TopicComposite & Inverse Functions

8 Functions f and g are defined as follows: $$\begin{aligned} & \mathrm { f } : x \mapsto x ^ { 2 } - 1 \text { for } x < 0
& \mathrm {~g} : x \mapsto \frac { 1 } { 2 x + 1 } \text { for } x < - \frac { 1 } { 2 } \end{aligned}$$
  1. Solve the equation \(\operatorname { fg } ( x ) = 3\).
  2. Find an expression for \(( \mathrm { fg } ) ^ { - 1 } ( x )\).