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3 marksAlgebraic Operations

CAPE Pure Mathematics Unit 1 · May/June 2002 · Paper 2 · Question 1(a)

A function f maps set A to set B, where A = {x ∈ R: x > 2} and B = {x ∈ R: x > 0}. The function is given by f(x) = 2x / (x - 2).

Find p, q ∈ R such that f(x) = p + q / (x - 2).

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Other parts of this question

  1. 1(b)Show that f is one-to-one.[6 marks]
  2. 1(c)Determine whether there is an x ∈ A such that f(x) = 1.[7 marks]
  3. 1(d)(i)Use Part (c) above to determine the range of f.[5 marks]
  4. 1(d)(ii)Use Part (c) above to determine whether or not f is onto.[4 marks]

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