CAIE P1 2012 June — Question 8

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2012
SessionJune
TopicComposite & Inverse Functions

8 The function \(\mathrm { f } : x \mapsto x ^ { 2 } - 4 x + k\) is defined for the domain \(x \geqslant p\), where \(k\) and \(p\) are constants.
  1. Express \(\mathrm { f } ( x )\) in the form \(( x + a ) ^ { 2 } + b + k\), where \(a\) and \(b\) are constants.
  2. State the range of f in terms of \(k\).
  3. State the smallest value of \(p\) for which f is one-one.
  4. For the value of \(p\) found in part (iii), find an expression for \(\mathrm { f } ^ { - 1 } ( x )\) and state the domain \(\mathrm { f } ^ { - 1 }\), giving your answers in terms of \(k\).