CAIE P1 2008 June — Question 6

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

6 The function f is such that \(\mathrm { f } ( x ) = ( 3 x + 2 ) ^ { 3 } - 5\) for \(x \geqslant 0\).
  1. Obtain an expression for \(\mathrm { f } ^ { \prime } ( x )\) and hence explain why f is an increasing function.
  2. Obtain an expression for \(\mathrm { f } ^ { - 1 } ( x )\) and state the domain of \(\mathrm { f } ^ { - 1 }\).