SPS SPS SM Pure 2023 September — Question 10

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

10. The functions f and g are defined by $$\begin{aligned} & \mathrm { f } ( x ) = 2 ^ { x } , x \in \mathbb { R }
& \mathrm {~g} ( x ) = \sqrt { 1 - x } , x \in \mathbb { R } , x \leq a \end{aligned}$$
  1. State the maximum possible value of \(a\).
  2. The function h is defined by \(\mathrm { h } ( x ) = \mathrm { gf } ( x )\)
    1. Write down an expression for \(\mathrm { h } ( x )\)
  3. (ii) Using set notation, state the greatest possible domain of h .
  4. (iii) State the range of h .