2023 IGCSE Additional Mathematics October/November 0606/21 Q9
2023 IGCSE Additional Mathematics October/November 0606/21 Q9
7 marks
The functions \(\mathrm{f}\) and \(\mathrm{g}\) are defined as follows, for all real values of \(x\).
\(\mathrm{f}(x)=2x^2-1\)
\(\mathrm{g}(x)=\mathrm{e}^x+1\)
- Solve the equation \(\mathrm{fg}(x)=8\).[3]
- For each of the functions \(\mathrm{f}\) and \(\mathrm{g}\), either explain why the inverse function does not exist or find the inverse function, stating its domain.[4]
Solution:
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Answer:(a) \(x=\ln\left(\dfrac{3}{\sqrt2}-1\right)=0.115\) (3 s.f.) (b) \(\mathrm{f}^{-1}\) does not exist because \(\mathrm{f}\) is not one-one; \(\mathrm{g}^{-1}(x)=\ln(x-1)\), domain \(x>1\)
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