2021 IGCSE Additional Mathematics May/June 0606/11 Q5
2021 IGCSE Additional Mathematics May/June 0606/11 Q5
7 marks
The functions \(\mathrm{f}\) and \(\mathrm{g}\) are defined as follows.
\(\mathrm{f}(x)=x^2+4x\quad\text{for}\hspace{0.5em}x\in\mathbb{R}\)
\(\mathrm{g}(x)=1+\mathrm{e}^{2x}\quad\text{for}\hspace{0.5em}x\in\mathbb{R}\)
- Find the range of \(\mathrm{f}\).[2]
- Write down the range of \(\mathrm{g}\).[1]
- Find the exact solution of the equation \(\mathrm{fg}(x)=21\), giving your answer as a single logarithm.[4]
Solution:
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Answer:(a) \(\mathrm{f}(x)\ge-4\) (b) \(\mathrm{g}(x)>1\) (c) \(x=\ln\sqrt2\)
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