OCR H240/01 2019 June — Question 3

Exam BoardOCR
ModuleH240/01 (Pure Mathematics)
Year2019
SessionJune
TopicComposite & Inverse Functions

3 The function f is defined by \(\mathrm { f } ( x ) = ( x - 3 ) ^ { 2 } - 17\) for \(x \geqslant k\), where \(k\) is a constant.
  1. Given that \(\mathrm { f } ^ { - 1 } ( x )\) exists, state the least possible value of \(k\).
  2. Evaluate \(\mathrm { ff } ( 5 )\).
  3. Solve the equation \(\mathrm { f } ( x ) = x\).
  4. Explain why your solution to part (c) is also the solution to the equation \(\mathrm { f } ( x ) = \mathrm { f } ^ { - 1 } ( x )\).