2020 IGCSE Additional Mathematics October/November 0606/11 Q7
2020 IGCSE Additional Mathematics October/November 0606/11 Q7
9 marks
It is given that \(\mathrm{f}(x)=5\ln(2x+3)\) for \(x>-\dfrac32\).
- Write down the range of \(\mathrm{f}\).[1]
- Find \(\mathrm{f}^{-1}\) and state its domain.[3]
- On the axes below, sketch the graph of \(y=\mathrm{f}(x)\) and the graph of \(y=\mathrm{f}^{-1}(x)\). Label each curve and state the intercepts on the coordinate axes.[5]
Solution:
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Answer:(a) \(\mathrm{f}(x)\in\mathbb{R}\) (b) \(\mathrm{f}^{-1}(x)=\dfrac{\mathrm{e}^{\frac{x}{5}}-3}{2}\), domain \(x\in\mathbb{R}\) (c) Sketch shown; \(y=\mathrm{f}(x)\) meets the axes at \((-1,0)\) and \((0,5\ln3)\); \(y=\mathrm{f}^{-1}(x)\) meets them at \((0,-1)\) and \((5\ln3,0)\)
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