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O-LevelAdditional MathematicsFunctions4037/12 · May/June 2020 · Q59 Marks

f: x → (2x+3)² for x > 0

  1. (a)Find the range of f.[1]
  2. (b)Explain why f has an inverse.[1]
  3. (c)Find f⁻¹.[3]
  4. (d)State the domain of f⁻¹.[1]
  5. (e)Given that g: x → ln(x+4) for x > 0, find the exact solution of fg(x) = 49.[3]

Mark scheme

Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.

  1. [1] f > 9
  2. [1] It is a one-one function because of the restricted domain
  3. [1] For a correct attempt to find the inverse
  4. [1] For correct rearrangement
  5. [1] Must have correct notation
  6. [1] x > 9
  7. [1] For correct order
  8. [1] For correct attempt to solve, dep on previous M mark, as far as x =
  9. [1] x = e²-4

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About this question

Topic
Functions, O-Level Additional Mathematics (syllabus 4037). Structured question, 9 marks.
Source
O-Level Additional Mathematics, May/June 2020 Paper 1 Variant 2, question 5.

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