OCR H240/03 2018 June — Question 4

Exam BoardOCR
ModuleH240/03 (Pure Mathematics and Mechanics)
Year2018
SessionJune
TopicComposite & Inverse Functions

4 In this question you must show detailed reasoning.
The functions f and g are defined for all real values of \(x\) by $$\mathrm { f } ( x ) = x ^ { 3 } \quad \text { and } \quad \mathrm { g } ( x ) = x ^ { 2 } + 2 .$$
  1. Write down expressions for
    (a) \(\mathrm { fg } ( x )\),
    (b) \(\operatorname { gf } ( x )\).
  2. Hence find the values of \(x\) for which \(\mathrm { fg } ( x ) - \mathrm { gf } ( x ) = 24\).