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O-LevelAdditional MathematicsFunctions4037/22 · Oct/Nov 2018 · Q119 Marks

The functions f and g are defined for real values of x ≥ 1 by f(x) = 4x-3, g(x) = (2x+1)/(3x-1).

  1. (i)Find gf(x).[2]
  2. (ii)Find g⁻¹(x).[3]
  3. (iii)Solve fg(x) = x-1.[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.

  1. [M1] gf(x) = 2(4x-3)+1 / 3(4x-3)-1
  2. [A1] 8x-5 / 12x-10
  3. [B1] y(3x-1)=2x+1 or x(3y-1)=2y+1
  4. [M1] (3y-2)x = y+1 or (3x-2)y=x+1
  5. [A1] g⁻¹(x) = x+1 / 3x-2
  6. [B1] 4(2x+1 / 3x-1) - 3 [= x-1]
  7. [B1] 3x²-3x-6 oe
  8. [M1] 3(x+1)(x-2)
  9. [A1] x = 2 only

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About this question

Topic
Functions, O-Level Additional Mathematics (syllabus 4037). Structured question, 9 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2018 Paper 2 Variant 2, question 11.

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