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3 marksFunctions

CAPE Pure Mathematics Unit 1 · May/June 2000 · Paper 2 · Question 2(a)(iii)

The function f is defined by f: x → x² - 2x + 3, x ∈ ℝ, x ≥ 1.

Explain why the inverse function f⁻¹ of f exists.

The mark scheme is shown once you've answered.

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Other parts of this question

  1. 2(a)(i)State the range of f.[3 marks]
  2. 2(a)(ii)Sketch the graph of f.[3 marks]
  3. 2(a)(iv)State the domain of f⁻¹.[2 marks]
  4. 2(a)(v)Sketch f⁻¹ on the same diagram as f.[4 marks]
  5. 2(b)State clearly the transformation which maps g onto f.[4 marks]
  6. 2(c)(i)Find an expression for f(h(x)).[3 marks]
  7. 2(c)(ii)Write down the range for the function f(h(x)).[3 marks]

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