CAIE P1 2023 November — Question 7

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2023
SessionNovember
TopicComposite & Inverse Functions

7 The function f is defined by \(\mathrm { f } ( x ) = 1 + \frac { 3 } { x - 2 }\) for \(x > 2\).
  1. State the range of f.
  2. Obtain an expression for \(\mathrm { f } ^ { - 1 } ( x )\) and state the domain of \(\mathrm { f } ^ { - 1 }\).
    The function g is defined by \(\mathrm { g } ( x ) = 2 x - 2\) for \(x > 0\).
  3. Obtain a simplified expression for \(\mathrm { gf } ( x )\).