CAIE P1 2017 November — Question 9

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

9 Functions f and g are defined for \(x > 3\) by $$\begin{aligned} & \mathrm { f } : x \mapsto \frac { 1 } { x ^ { 2 } - 9 }
& \mathrm {~g} : x \mapsto 2 x - 3 \end{aligned}$$
  1. Find and simplify an expression for \(\operatorname { gg } ( x )\).
  2. Find an expression for \(\mathrm { f } ^ { - 1 } ( x )\) and state the domain of \(\mathrm { f } ^ { - 1 }\).
  3. Solve the equation \(\operatorname { fg } ( x ) = \frac { 1 } { 7 }\).