CAIE P1 2020 November — Question 6

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2020
SessionNovember
TopicComposite & Inverse Functions

6 The function f is defined by \(\mathrm { f } ( x ) = \frac { 2 x } { 3 x - 1 }\) for \(x > \frac { 1 } { 3 }\).
  1. Find an expression for \(\mathrm { f } ^ { - 1 } ( x )\).
  2. Show that \(\frac { 2 } { 3 } + \frac { 2 } { 3 ( 3 x - 1 ) }\) can be expressed as \(\frac { 2 x } { 3 x - 1 }\).
  3. State the range of f.