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4 marksFunctions

CAPE Pure Mathematics Unit 1 · May/June 1999 · Paper 2 · Question 2(a)(ii)

The function f is defined by f: x → 1 - 6x - 3x², x ∈ R.

Calculate the exact values of x which map onto themselves under the function f.

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Other parts of this question

  1. 2(a)(i)Evaluate f(-2).[2 marks]
  2. 2(a)(iii)Express f(x) in the form u(x - v)² + w, where u, v, w ∈ R.[3 marks]
  3. 2(a)(iv)By sketching the graph of y = f(x), or otherwise, state the turning point P of the graph and indicate whether P is a maximum or a minimum.[3 marks]
  4. 2(b)(i)Determine the range of f.[1 mark]
  5. 2(b)(ii)Explain why the function f has an inverse.[1 mark]
  6. 2(b)(iii)Find an expression for f⁻¹(x).[4 marks]
  7. 2(b)(iv)Describe the geometrical relationship between the graphs y = f(x) and y = f⁻¹(x).[2 marks]

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