CAIE P1 2011 June — Question 6

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

6 The function f is defined by \(\mathrm { f } : x \mapsto \frac { x + 3 } { 2 x - 1 } , x \in \mathbb { R } , x \neq \frac { 1 } { 2 }\).
  1. Show that \(\operatorname { ff } ( x ) = x\).
  2. Hence, or otherwise, obtain an expression for \(\mathrm { f } ^ { - 1 } ( x )\).