SPS SPS SM Pure 2023 February — Question 9

Exam BoardSPS
ModuleSPS SM Pure (SPS SM Pure)
Year2023
SessionFebruary
TopicComposite & Inverse Functions

9. The function g is defined by $$\mathrm { g } : x \mapsto | 8 - 2 x | , \quad x \in \mathbb { R } , \quad x \geqslant 0$$
  1. Sketch the graph with equation \(y = \mathrm { g } ( x )\), showing the coordinates of the points where the graph cuts or meets the axes.
    (2)
  2. Solve the equation $$| 8 - 2 x | = x + 5$$ The function \(f\) is defined by $$\mathrm { f } : x \mapsto x ^ { 2 } - 3 x + 1 , \quad x \in \mathbb { R } , \quad 0 \leqslant x \leqslant 4$$
  3. Find fg(5).
  4. Find the range of f . You must make your method clear.