SPS SPS FM 2023 October — Question 6

Exam BoardSPS
ModuleSPS FM (SPS FM)
Year2023
SessionOctober
TopicBinomial Theorem (positive integer n)
TypeSubstitution into binomial expansion

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