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3 marksFunctions

CAPE Pure Mathematics Unit 1 · May/June 2003 · Paper 2 · Question 2(b)(ii)

Two sets, A and B, are defined on ℝ as follows: A = {x: 0 ≤ x ≤ 4}, B = {x: 0 ≤ x ≤ 8}. The function f: A → B is defined by f: x → x(4 - x).

Find a set C such that C ⊂ A and f: C → B, is one-to-one.

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Other parts of this question

  1. 2(a)(i)Use this diagram to assist you in sketching the function x = f(x - 1).[3 marks]
  2. 2(a)(ii)Use this diagram to assist you in sketching the function y = f(x) + 3.[3 marks]
  3. 2(a)(iii)Use this diagram to assist you in sketching the function y = |f(x)|.[3 marks]
  4. 2(b)(i)Sketch the graph of f: A → B.[3 marks]
  5. 2(b)(iii)By considering the solutions of the equation f(x) = 8, show that f is NOT onto.[4 marks]
  6. 2(b)(iv)By solving the equation f(x) = 0, show that f: A → B is NOT one-to-one.[4 marks]
  7. 2(b)(v)Find the range of values of y for which the equation f(x) = y possesses a solution.[2 marks]

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