| Exam Board | AQA |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2012 |
| Session | January |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | Solve equation involving composites |
| Difficulty | Moderate -0.3 This is a standard C3 question on inverse functions and composites requiring routine techniques: finding range from endpoints, algebraic manipulation to find inverse, substitution for composite function, and solving simple equations. All steps are textbook exercises 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 |
2 The curve with equation $y = \frac { 63 } { 4 x - 1 }$ is sketched below for $1 \leqslant x \leqslant 16$.\\
\includegraphics[max width=\textwidth, alt={}, center]{7aa76d26-e3c4-4374-ae4f-8bb61e61b135-2_568_698_1308_669}
The function f is defined by $\mathrm { f } ( x ) = \frac { 63 } { 4 x - 1 }$ for $1 \leqslant x \leqslant 16$.
\begin{enumerate}[label=(\alph*)]
\item Find the range of f .
\item The inverse of f is $\mathrm { f } ^ { - 1 }$.
\begin{enumerate}[label=(\roman*)]
\item Find $\mathrm { f } ^ { - 1 } ( x )$.
\item Solve the equation $\mathrm { f } ^ { - 1 } ( x ) = 1$.
\end{enumerate}\item The function g is defined by $\mathrm { g } ( x ) = x ^ { 2 }$ for $- 4 \leqslant x \leqslant - 1$.
\begin{enumerate}[label=(\roman*)]
\item Write down an expression for $\mathrm { fg } ( x )$.
\item Solve the equation $\operatorname { fg } ( x ) = 1$.
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{AQA C3 2012 Q2 [11]}}