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2020 IGCSE Additional Mathematics October/November 0606/12 Q6

2020 IGCSE Additional Mathematics October/November 0606/12 Q6

5 marks

\(\mathrm{f}(x)=x^2+2x-3\quad\text{for}\hspace{0.5em}x\ge-1\)

  1. Given that the minimum value of \(x^2+2x-3\) occurs when \(x=-1\), explain why \(\mathrm{f}(x)\) has an inverse.[1]
  2. On the axes below, sketch the graph of \(y=\mathrm{f}(x)\) and the graph of \(y=\mathrm{f}^{-1}(x)\). Label each graph and state the intercepts on the coordinate axes.[4]

Solution:

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Answer:(a) \(\mathrm{f}\) is one-one because its domain \(x\ge-1\) starts at the minimum point, so \(\mathrm{f}\) is increasing (b) Sketch shown; \(y=\mathrm{f}(x)\): intercepts \((1,0)\) and \((0,-3)\); \(y=\mathrm{f}^{-1}(x)\): reflection in \(y=x\), intercepts \((-3,0)\) and \((0,1)\)

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