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O-LevelAdditional MathematicsFunctions4037/11 · May/June 2010 · Q78 Marks

The function f is defined by f(x) = (2x + 1)² - 3 for x = -1/2.

  1. (i)Find the range of f,[1]
  2. (ii)an expression for f¯¹ (x).[3]
  3. (iii)The function g is defined by g(x) = 3 / (1+x) for x > -1. Find the value of x for which fg(x) = 13.[4]

Mark scheme

Marking points from the official mark scheme (May/June 2010). The mark or mark type is shown in brackets.

  1. [1] (i) B1 for f >= -3
  2. [3] (ii) M1 for correct order of operations; M1 for 'interchange' of x and y; A1 for (sqrt(x+3)-1)/2
  3. [4] (iii) M1 for correct order of operations (substitution of g(x) into f(x)); A1 for correct simplification; M1 for solution leading to x=1; B1 for one solution only

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About this question

Topic
Functions, O-Level Additional Mathematics (syllabus 4037). Structured question, 8 marks.
Source
O-Level Additional Mathematics, May/June 2010 Paper 1 Variant 1, question 7.

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