CAIE P1 2023 March — Question 9

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

9 The function f is defined by \(\mathrm { f } ( x ) = - 3 x ^ { 2 } + 2\) for \(x \leqslant - 1\).
  1. State the range of f.
  2. Find an expression for \(\mathrm { f } ^ { - 1 } ( x )\).
    The function g is defined by \(\mathrm { g } ( x ) = - x ^ { 2 } - 1\) for \(x \leqslant - 1\).
  3. Solve the equation \(\mathrm { fg } ( x ) - \mathrm { gf } ( x ) + 8 = 0\).