CAIE P1 2011 November — Question 2

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2011
SessionNovember
TopicComposite & Inverse Functions

2 The functions f and g are defined for \(x \in \mathbb { R }\) by $$\begin{aligned} & \mathrm { f } : x \mapsto 3 x + a
& \mathrm {~g} : x \mapsto b - 2 x \end{aligned}$$ where \(a\) and \(b\) are constants. Given that \(\mathrm { ff } ( 2 ) = 10\) and \(\mathrm { g } ^ { - 1 } ( 2 ) = 3\), find
  1. the values of \(a\) and \(b\),
  2. an expression for \(\mathrm { fg } ( x )\).