| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2013 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | Sketch function and inverse graphs |
| Difficulty | Moderate -0.3 Part (a) is routine algebraic simplification of a rational function. Part (b) requires standard transformations (stretch) and reflection in y=x for the inverse, with coordinate transformations that follow directly from A-level rules. While multi-part, each component uses well-practiced techniques without requiring novel problem-solving insight. |
| Spec | 1.02k Simplify rational expressions: factorising, cancelling, algebraic division1.02v Inverse and composite functions: graphs and conditions for existence1.02w Graph transformations: simple transformations of f(x) |
1.
$$g ( x ) = \frac { 6 x + 12 } { x ^ { 2 } + 3 x + 2 } - 2 , \quad x \geqslant 0$$
\begin{enumerate}[label=(\alph*)]
\item Show that $\mathrm { g } ( x ) = \frac { 4 - 2 x } { x + 1 } , x \geqslant 0$
\item \begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{0f6fd881-4d4b-4f80-96cc-6da41cc33c60-02_494_922_628_511}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
Figure 1 shows a sketch of the curve with equation $y = \mathrm { g } ( x ) , x \geqslant 0$
The curve meets the $y$-axis at $( 0,4 )$ and crosses the $x$-axis at $( 2,0 )$.
On separate diagrams sketch the graph with equation
\begin{enumerate}[label=(\roman*)]
\item $y = 2 \mathrm {~g} ( 2 x )$,
\item $y = \mathrm { g } ^ { - 1 } ( x )$.
Show on each sketch the coordinates of each point at which the graph meets or crosses the axes.
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{Edexcel C3 2013 Q1 [8]}}