2021 SJI P1 Q1

2021 SJI P1 Q1

IB Year 5 | Grade 11
5 marks

Define a function \(\mathrm{f}\), including its maximal domain, such that its inverse exists and is given by

\[\mathrm{f}^{-1}(x)=\frac{\mathrm{e}^x}{\mathrm{e}^x-1},\quad x\neq0,\ x\in\mathbb R.\][5]

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Answer:\(\mathrm{f}(x)=\ln\left(\dfrac{x}{x-1}\right),\ x<0\text{ or}\hspace{0.5em}x>1\)

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