AQA Paper 2 2023 June — Question 7

Exam BoardAQA
ModulePaper 2 (Paper 2)
Year2023
SessionJune
TopicComposite & Inverse Functions

7 The functions f and g are defined by $$\begin{aligned} & \mathrm { f } ( x ) = \sqrt { 10 - 2 x } \text { for } \quad x \leq 5
& \mathrm {~g} ( x ) = \frac { 1 } { x } \quad \text { for } \quad x \neq 0 \end{aligned}$$ The function \(h\) has maximum possible domain and is defined by $$\mathrm { h } ( x ) = \operatorname { gf } ( x )$$ 7
  1. Find an expression for \(\mathrm { h } ( x )\)
    7
  2. Find the domain of h
    7
  3. Show that \(\mathrm { h } ^ { - 1 } ( x ) = 5 - \frac { 1 } { 2 x ^ { 2 } }\)
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