| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2008 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | Find composite function expression |
| Difficulty | Easy -1.2 This is a straightforward composite function question requiring only direct substitution (fg(x) = (x-2)² and gf(x) = x²-2) followed by sketching three parabolas with simple transformations. It tests basic function composition and graph transformations with no problem-solving or novel insight required—significantly easier than average A-level questions. |
| Spec | 1.02u Functions: definition and vocabulary (domain, range, mapping)1.02v Inverse and composite functions: graphs and conditions for existence1.02w Graph transformations: simple transformations of f(x) |
2 The functions $\mathrm { f } ( x )$ and $\mathrm { g } ( x )$ are defined for all real numbers $x$ by
$$\mathrm { f } ( x ) = x ^ { 2 } , \quad \mathrm {~g} ( x ) = x - 2$$
(i) Find the composite functions $\mathrm { fg } ( x )$ and $\mathrm { gf } ( x )$.\\
(ii) Sketch the curves $y = \mathrm { f } ( x ) , y = \mathrm { fg } ( x )$ and $y = \mathrm { gf } ( x )$, indicating clearly which is which.
\hfill \mbox{\textit{OCR MEI C3 2008 Q2 [5]}}