CAIE P1 2020 November — Question 5

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2020
SessionNovember
TopicComposite & Inverse Functions

5 Functions f and g are defined by $$\begin{aligned} & \mathrm { f } ( x ) = 4 x - 2 , \quad \text { for } x \in \mathbb { R } ,
& \mathrm {~g} ( x ) = \frac { 4 } { x + 1 } , \quad \text { for } x \in \mathbb { R } , x \neq - 1 \end{aligned}$$
  1. Find the value of fg (7).
  2. Find the values of \(x\) for which \(\mathrm { f } ^ { - 1 } ( x ) = \mathrm { g } ^ { - 1 } ( x )\).