| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | Determine domain for composite |
| Difficulty | Standard +0.3 This is a straightforward composite functions question requiring basic evaluation of trigonometric and quadratic functions, range identification, and domain analysis. Part (i) is routine recall, part (ii) involves simple substitution and calculator work, and part (iii) requires understanding that f^{-1} needs inputs in [-2,2], leading to a quadratic inequality. All techniques are standard C3 material with no novel insight required, making it slightly easier than average. |
| Spec | 1.02u Functions: definition and vocabulary (domain, range, mapping)1.02v Inverse and composite functions: graphs and conditions for existence |
Functions f and g are defined by
$$f(x) = 2 \sin x \quad \text{for } -\frac{1}{2}\pi \leq x \leq \frac{1}{2}\pi,$$
$$g(x) = 4 - 2x^2 \quad \text{for } x \in \mathbb{R}.$$
\begin{enumerate}[label=(\roman*)]
\item State the range of f and the range of g. [2]
\item Show that gf(0.5) = 2.16, correct to 3 significant figures, and explain why fg(0.5) is not defined. [4]
\item Find the set of values of $x$ for which $f^{-1}g(x)$ is not defined. [6]
\end{enumerate}
\hfill \mbox{\textit{OCR C3 Q9 [12]}}