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7 marksFunctions

CAPE Pure Mathematics Unit 1 · May/June 2013 · Paper 2 · Question 2(a)

Let A = {x: x ∈ R, x ≥ 1}. A function f: A → R is defined as f(x) = x² - x.

Show that f is one to one.

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Other parts of this question

  1. 2(b)(i)Find[1 mark]
  2. 2(b)(i)a)f⁻¹(x) and g⁻¹(x)[4 marks]
  3. 2(b)(i)b)f [g(x)] (or f∘g(x)).[1 mark]
  4. 2(b)(ii)Show that (f∘g)⁻¹ (x) = g⁻¹ (x) ∘ f⁻¹ (x).[5 marks]
  5. 2(c)Solve the following:[1 mark]
  6. 2(c)(i)3x² + 4x +1 ≤ 5[4 marks]
  7. 2(c)(ii)|x + 2| = 3x + 5[4 marks]

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