| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2009 |
| Session | January |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | Verify composite identity |
| Difficulty | Moderate -0.8 This is a straightforward verification task requiring students to show either f(g(x)) = x or g(f(x)) = x using basic logarithm and exponential rules. The algebraic manipulation is routine with no problem-solving required—students simply substitute and simplify using standard C3 techniques. Easier than average as it's purely mechanical verification rather than finding or deriving inverses. |
| Spec | 1.02v Inverse and composite functions: graphs and conditions for existence1.06d Natural logarithm: ln(x) function and properties1.06e Logarithm as inverse: ln(x) inverse of e^x |
3 Given that $\mathrm { f } ( x ) = \frac { 1 } { 2 } \ln ( x - 1 )$ and $\mathrm { g } ( x ) = 1 + \mathrm { e } ^ { 2 x }$, show that $\mathrm { g } ( x )$ is the inverse of $\mathrm { f } ( x )$.
\hfill \mbox{\textit{OCR MEI C3 2009 Q3 [3]}}