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6 marksThe Modulus Function

CAPE Pure Mathematics Unit 1 · May/June 2015 · Paper 2 · Question 2(b)(ii)

The diagrams below (not drawn to scale) show the graphs of f(x) = x² - 4x + 3 and g(x) = 2 - 3x.

Hence, or otherwise, solve the equation |x² – 4x + 3| = |2 – 3x|.

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Other parts of this question

  1. 2(a)(i)Show that 1/logₐx may be rewritten as ln a / ln x, where a > 0, a ≠ 1.[5 marks]
  2. 2(a)(ii)Hence, or otherwise, solve the equation: 1/log₂x + 1/log₃x + 1/log₄x + 1/log₅x = 1.[4 marks]
  3. 2(b)(i)On the same axes, sketch the graphs |f(x)| and |g(x)|.[4 marks]
  4. 2(c)Determine the value of f(f⁻¹[f(1)]).[6 marks]

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