| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | Find inverse function |
| Difficulty | Moderate -0.3 This is a straightforward C3 inverse functions question with standard components: evaluating a composite function (routine substitution), finding an inverse (rearranging a quadratic with restricted domain), and sketching the reflection. All parts follow textbook procedures with no problem-solving required, making it slightly easier than average but not trivial due to the multi-step nature and need for careful domain handling. |
| Spec | 1.02u Functions: definition and vocabulary (domain, range, mapping)1.02v Inverse and composite functions: graphs and conditions for existence |
\includegraphics{figure_6}
The diagram shows the graph of $y = f(x)$, where
$$f(x) = 2 - x^2, \quad x \leq 0.$$
\begin{enumerate}[label=(\roman*)]
\item Evaluate ff(-3). [3]
\item Find an expression for $f^{-1}(x)$. [3]
\item Sketch the graph of $y = f^{-1}(x)$. Indicate the coordinates of the points where the graph meets the axes. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR C3 Q6 [9]}}