| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2011 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | Find inverse function |
| Difficulty | Standard +0.3 This question tests standard C3 content on inverse trigonometric functions and their inverses. Part (i) requires knowing the range of arctan (which is -π/2 to π/2) and applying a simple transformation. Part (ii) involves routine algebraic manipulation to find the inverse function and sketching by reflection in y=x. While it requires understanding of arctan properties, the techniques are straightforward and commonly practiced, making it slightly easier than average. |
| Spec | 1.02v Inverse and composite functions: graphs and conditions for existence1.05i Inverse trig functions: arcsin, arccos, arctan domains and graphs |
Fig. 7 shows the curve $y = f(x)$, where $f(x) = 1 + 2 \arctan x$, $x \in \mathbb{R}$. The scales on the $x$- and $y$-axes are the same.
\includegraphics{figure_7}
\begin{enumerate}[label=(\roman*)]
\item Find the range of f, giving your answer in terms of $\pi$.
[3]
\item Find $f^{-1}(x)$, and add a sketch of the curve $y = f^{-1}(x)$ to the copy of Fig. 7.
[5]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C3 2011 Q7 [8]}}