| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | Find composite function expression |
| Difficulty | Moderate -0.8 This is a straightforward composite function question requiring basic substitution (fg(x) = (x-2)² and gf(x) = x²-2) followed by sketching three parabolas. It involves only routine algebraic manipulation and standard curve sketching with no problem-solving insight required, making it easier than average. |
| Spec | 1.02n Sketch curves: simple equations including polynomials1.02v Inverse and composite functions: graphs and conditions for existence |
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 Q2 [5]}}