2022 IGCSE Additional Mathematics May/June 0606/11 Q3
2022 IGCSE Additional Mathematics May/June 0606/11 Q3
10 marks
A function \(\mathrm{f}\) is such that \(\mathrm{f}(x)=\ln(2x+1)\), for \(x>-\dfrac12\).
- Write down the range of \(\mathrm{f}\).[1]
A function \(\mathrm{g}\) is such that \(\mathrm{g}(x)=5x-7\), for \(x\in\mathbb{R}\).
- Find the exact solution of the equation \(\mathrm{gf}(x)=13\).[3]
- Find the solution of the equation \(\mathrm{f}'(x)=\mathrm{g}^{-1}(x)\).[6]
Solution:
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Answer:(a) \(\mathrm{f}(x)\in\mathbb{R}\) (b) \(x=\dfrac{\mathrm{e}^4-1}{2}\) (c) \(x=\dfrac{-15+\sqrt{249}}{4}=0.195\) (3 s.f.); \(x=-7.69\) is rejected because \(x>-\dfrac12\)
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