CAIE P1 2008 June — Question 8

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2008
SessionJune
TopicComposite & Inverse Functions

8 Functions f and g are defined by $$\begin{array} { l l } \mathrm { f } : x \mapsto 4 x - 2 k & \text { for } x \in \mathbb { R } , \text { where } k \text { is a constant, }
\mathrm { g } : x \mapsto \frac { 9 } { 2 - x } & \text { for } x \in \mathbb { R } , x \neq 2 . \end{array}$$
  1. Find the values of \(k\) for which the equation \(\mathrm { fg } ( x ) = x\) has two equal roots.
  2. Determine the roots of the equation \(\operatorname { fg } ( x ) = x\) for the values of \(k\) found in part (i).