2023 IGCSE Additional Mathematics October/November 0606/23 Q1
2023 IGCSE Additional Mathematics October/November 0606/23 Q1
6 marks
The functions \(\mathrm{f}\) and \(\mathrm{g}\) are defined as follows, for all real values of \(x\).
\(\mathrm{f}(x)=2\sin x+3\cos x\)
\(\mathrm{g}(x)=\mathrm{e}^{3x}-1\)
- Find \(\mathrm{fg}(0)\).[2]
- Find \(\mathrm{gg}(x)\).[1]
- Solve the equation \(\mathrm{g}^{-1}(x)=\dfrac13\ln5\).[3]
Solution:
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Answer:(a) \(\mathrm{fg}(0)=3\) (b) \(\mathrm{gg}(x)=\mathrm{e}^{3\left(\mathrm{e}^{3x}-1\right)}-1\) (c) \(x=4\)
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