| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | State domain or range |
| Difficulty | Moderate -0.3 This is a straightforward C3 question testing basic function concepts. Part (i) requires reading the range from a given graph (routine). Part (ii) is a simple composition calculation: f(4)=0, then f(0)=2. Part (iii) requires understanding when |f(x)|=k has two solutions by considering the graph of y=|f(x)|, concluding k>0. All parts are standard textbook exercises with no novel problem-solving required, making this slightly easier than average. |
| Spec | 1.02l Modulus function: notation, relations, equations and inequalities1.02u Functions: definition and vocabulary (domain, range, mapping) |
\includegraphics{figure_4}
The function f is defined by $f(x) = 2 - \sqrt{x}$ for $x \geq 0$. The graph of $y = f(x)$ is shown above.
\begin{enumerate}[label=(\roman*)]
\item State the range of f. [1]
\item Find the value of ff(4). [2]
\item Given that the equation $|f(x)| = k$ has two distinct roots, determine the possible values of the constant $k$. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR C3 Q4 [5]}}