June 2024 Paper 1 Q2
2 The function \(\mathrm{f}\) is defined by \(\mathrm{f}(x) = \mathrm{e}^x + 1\) for \(x \in \mathbb{R}\)
Find an expression for \(\mathrm{f}^{-1}(x)\)
Tick (✓) one box. [1 mark]
- \(\mathrm{f}^{-1}(x) = \ln(x-1)\)
- \(\mathrm{f}^{-1}(x) = \ln(x) - 1\)
- \(\mathrm{f}^{-1}(x) = \frac{1}{\mathrm{e}^x + 1}\)
- \(\mathrm{f}^{-1}(x) = \frac{x-1}{\mathrm{e}}\)
| Scheme | Marks | AO |
|---|---|---|
| Ticks the 1st box | B1 | 1.1b |
| (1 mark) |
Typical solution
\(\mathrm{f}^{-1}(x) = \ln(x-1)\)