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6 marksFunctions

CAPE Pure Mathematics Unit 1 · May/June 2012 · Paper 2 · Question 2(a)(ii)

The function f on R is defined by f: x → x²-3.

Determine the values of x for which f(f(x)) = f(x + 3).

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Other parts of this question

  1. 2(a)Find[1 mark]
  2. 2(a)(i)in terms of x, f(f(x)).[3 marks]
  3. 2(b)(i)write down the values of α + β and αβ[2 marks]
  4. 2(b)(ii)find the value of α² + β²[2 marks]
  5. 2(b)(iii)obtain a quadratic equation whose roots are 2/α² and 2/β².[5 marks]
  6. 2(c)Without the use of calculators or tables, evaluate[1 mark]
  7. 2(c)(i)log₁₀(1/3) + log₁₀(3/5) + log₁₀(5/7) + log₁₀(7/9) + log₁₀(9/10)[3 marks]
  8. 2(c)(ii)∑_{r=1}^{99} log₁₀(r/(r+1)).[4 marks]

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