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2025 IGCSE Additional Mathematics February/March 0606/12 Q5

2025 IGCSE Additional Mathematics February/March 0606/12 Q5

8 marks
  1. Write \(2x^2-2x+3\) in the form \(a(x+b)^2+c\), where \(a\), \(b\) and \(c\) are constants.[3]

It is given that \(\mathrm{f}(x)=2x^2-2x+3\), for \(x\le p\).

  1. Write down the greatest value of \(p\) for which \(\mathrm{f}\) has an inverse.[1]
  2. Using this value of \(p\), write down the range of \(\mathrm{f}\).[1]
  3. Using this value of \(p\), find an expression for \(\mathrm{f}^{-1}\).[3]

Solution:

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Answer:(a) \(2\left(x-\dfrac12\right)^2+\dfrac52\) (b) \(p=\dfrac12\) (c) \(\mathrm{f}(x)\ge\dfrac52\) (d) \(\mathrm{f}^{-1}(x)=\dfrac{1-\sqrt{2x-5}}2\)

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