| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | Evaluate composite at point |
| Difficulty | Moderate -0.8 This is a straightforward function composition and inverse function question requiring only basic substitution and solving a simple cubic equation. Both parts are routine C3 exercises with minimal steps: (i) substitute x=1 into g, then into f; (ii) solve x³+4=12 to get x=2. No problem-solving insight needed, just direct application of definitions. |
| Spec | 1.02v Inverse and composite functions: graphs and conditions for existence |
Functions f and g are defined for all real values of $x$ by
$$f(x) = x^3 + 4 \quad \text{and} \quad g(x) = 2x - 5.$$
Evaluate
\begin{enumerate}[label=(\roman*)]
\item fg(1), [2]
\item $f^{-1}(12)$. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR C3 Q1 [5]}}