AQA Paper 1 Specimen — Question 10 10 marks

Exam BoardAQA
ModulePaper 1 (Paper 1)
SessionSpecimen
Marks10
TopicComposite & Inverse Functions

10 The function f is defined by $$\mathrm { f } ( x ) = 4 + 3 ^ { - x } , x \in \mathbb { R }$$ 10
  1. Using set notation, state the range of f
    [0pt] [2 marks]
    10
  2. The inverse of f is \(\mathrm { f } ^ { - 1 }\) 10
    1. Using set notation, state the domain of \(f ^ { - 1 }\)
      [0pt] [1 mark]
      10
  3. (ii) Find an expression for \(\mathrm { f } ^ { - 1 } ( x )\)
    [0pt] [3 marks]
    10
  4. The function \(g\) is defined by $$g ( x ) = 5 - \sqrt { x } , ( x \in \mathbb { R } : x > 0 )$$ 10
    1. Find an expression for gf (x)
      [0pt] [1 mark]
      10
  5. (ii) Solve the equation \(\mathrm { gf } ( x ) = 2\), giving your answer in an exact form.
    [0pt] [3 marks]