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