| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2010 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | Find inverse function |
| Difficulty | Moderate -0.8 This is a straightforward C3 question testing basic function operations. Part (i) is simple substitution, (ii) requires understanding when a function equals its absolute value (when non-negative), (iii) is standard inverse function procedure, and (iv) is recall of the reflection property. All parts are routine textbook exercises with no problem-solving or novel insight required, making it easier than average. |
| Spec | 1.02l Modulus function: notation, relations, equations and inequalities1.02v Inverse and composite functions: graphs and conditions for existence |
\includegraphics{figure_4}
The function $f$ is defined for all real values of $x$ by
$$f(x) = 2 - \sqrt{x + 1}.$$
The diagram shows the graph of $y = f(x)$.
\begin{enumerate}[label=(\roman*)]
\item Evaluate $f(-126)$. [2]
\item Find the set of values of $x$ for which $f(x) = |f(x)|$. [2]
\item Find an expression for $f^{-1}(x)$. [3]
\item State how the graphs of $y = f(x)$ and $y = f^{-1}(x)$ are related geometrically. [1]
\end{enumerate}
\hfill \mbox{\textit{OCR C3 2010 Q4 [8]}}