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3 marksFunctions

CAPE Pure Mathematics Unit 1 · May/June 2001 · Paper 2 · Question 1(d)(i)

The functions, f and g, are defined by f: x → x²/(1-x²), x² ≠ 1, and g: x → x - 1/2 - 3.

Explain clearly why f is not 1 – 1.

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Other parts of this question

  1. 1(a)Show that the inequality |x-3| ≥ |x-3| holds for any x ∈ R.[4 marks]
  2. 1(b)Factorise completely the polynomial, x³ + 2x² - x - 2.[4 marks]
  3. 1(c)Find the value of r such that x⁴ - 7x + 4r has a remainder -2 when it is divided by x + 3.[4 marks]
  4. 1(d)(ii)Calculate and simplify g f(x).[5 marks]
  5. 1(e)(i)Using a scale of 2 cm to represent 10 minutes on the x-axis and 2 cm to represent 20 bacteria on the y-axis, draw the growth curve for the treatment stage.[4 marks]
  6. 1(e)(ii)Hence, estimate the number of bacteria present after the first 35 minutes of treatment.[1 mark]

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