| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | Verify composite identity |
| Difficulty | Moderate -0.3 This question tests basic definitions of odd/even functions and requires a straightforward proof by substitution. While it involves function composition, the proof is mechanical once the definitions are recalled—no novel insight or complex manipulation is needed. Slightly easier than average due to its direct nature and limited steps. |
| Spec | 1.02u Functions: definition and vocabulary (domain, range, mapping)1.02v Inverse and composite functions: graphs and conditions for existence |
Write down the conditions for f(x) to be an odd function and for g(x) to be an even function.
Hence prove that, if f(x) is odd and g(x) is even, then the composite function gf(x) is even. [4]
\hfill \mbox{\textit{OCR MEI C3 Q5 [4]}}