CAIE P1 2019 June — Question 7 4 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2019
SessionJune
Marks4
TopicComposite & Inverse Functions

7 Functions f and g are defined by $$\begin{aligned} & \mathrm { f } : x \mapsto 3 x - 2 , \quad x \in \mathbb { R } ,
& \mathrm {~g} : x \mapsto \frac { 2 x + 3 } { x - 1 } , \quad x \in \mathbb { R } , x \neq 1 \end{aligned}$$
  1. Obtain expressions for \(\mathrm { f } ^ { - 1 } ( x )\) and \(\mathrm { g } ^ { - 1 } ( x )\), stating the value of \(x\) for which \(\mathrm { g } ^ { - 1 } ( x )\) is not defined. [4]
  2. Solve the equation \(\operatorname { fg } ( x ) = \frac { 7 } { 3 }\).