| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | Verify composite identity |
| Difficulty | Moderate -0.5 This is a straightforward verification question requiring students to show gf(x) = x and fg(x) = x using basic logarithm and exponential properties. It's slightly easier than average because it's purely algebraic manipulation with no problem-solving required, though it does test understanding of inverse functions and the relationship between ln and e. |
| Spec | 1.02v Inverse and composite functions: graphs and conditions for existence1.06a Exponential function: a^x and e^x graphs and properties1.06d Natural logarithm: ln(x) function and properties |
Given that $f(x) = \frac{1}{2}\ln(x - 1)$ and $g(x) = 1 + e^{2x}$, show that g(x) is the inverse of f(x). [3]
\hfill \mbox{\textit{OCR MEI C3 Q7 [3]}}