2026 IGCSE Additional Mathematics February/March 0606/12 Q2

2026 IGCSE Additional Mathematics February/March 0606/12 Q2

6 marks
  1. On the axes, sketch the graph of \(y=\left|x^2-2x-3\right|\).
    State the intercepts with the coordinate axes.[4]
  2. The function \(\mathrm{g}\) is defined by \(\mathrm{g}(x)=4e^{x-2}-1\) for all real \(x\).
    Find an expression for \(\mathrm{g}^{-1}(x)\).[2]

Solution:

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Answer:(a) Intercepts \((-1,0),(3,0),(0,3)\); graph shown in the solution. (b) \(\mathrm{g}^{-1}(x)=2+\ln\left(\dfrac{x+1}{4}\right)\), \(x>-1\)

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