CAIE P1 2022 June — Question 6

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2022
SessionJune
TopicComposite & Inverse Functions

6 The function f is defined by \(\mathrm { f } ( x ) = 2 x ^ { 2 } - 16 x + 23\) for \(x < 3\).
  1. Express \(\mathrm { f } ( x )\) in the form \(2 ( x + a ) ^ { 2 } + b\).
  2. Find the range of f.
  3. Find an expression for \(\mathrm { f } ^ { - 1 } ( x )\).
    The function g is defined by \(\mathrm { g } ( x ) = 2 x + 4\) for \(x < - 1\).
  4. Find and simplify an expression for \(\mathrm { fg } ( x )\).