| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2008 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | Evaluate composite at point |
| Difficulty | Easy -1.2 This is a straightforward question testing basic function composition and inverse function evaluation. Part (i) requires substituting x=1 into g, then that result into f—a simple two-step calculation. Part (ii) involves solving a cubic equation (x³+4=12) which simplifies to x³=8, giving x=2. Both parts are routine applications of definitions with minimal problem-solving required, making this easier than average. |
| Spec | 1.02v Inverse and composite functions: graphs and conditions for existence |
1 Functions f and g are defined for all real values of $x$ by
$$\mathrm { f } ( x ) = x ^ { 3 } + 4 \quad \text { and } \quad \mathrm { g } ( x ) = 2 x - 5$$
Evaluate\\
(i) $f g ( 1 )$,\\
(ii) $\mathrm { f } ^ { - 1 } ( 12 )$.
\hfill \mbox{\textit{OCR C3 2008 Q1 [5]}}