CAIE P1 2013 June — Question 10

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2013
SessionJune
TopicComposite & Inverse Functions

10 The function f is defined by \(\mathrm { f } : x \mapsto 2 x + k , x \in \mathbb { R }\), where \(k\) is a constant.
  1. In the case where \(k = 3\), solve the equation \(\mathrm { ff } ( x ) = 25\). The function g is defined by \(\mathrm { g } : x \mapsto x ^ { 2 } - 6 x + 8 , x \in \mathbb { R }\).
  2. Find the set of values of \(k\) for which the equation \(\mathrm { f } ( x ) = \mathrm { g } ( x )\) has no real solutions. The function \(h\) is defined by \(h : x \mapsto x ^ { 2 } - 6 x + 8 , x > 3\).
  3. Find an expression for \(\mathrm { h } ^ { - 1 } ( x )\).