| Exam Board | AQA |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2012 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | Solve equation involving composites |
| Difficulty | Moderate -0.3 This is a straightforward multi-part question testing standard C3 composite and inverse function techniques. All parts involve routine procedures: stating range from a square root function, composing functions by substitution, solving a simple equation, finding an inverse by swapping and rearranging, and evaluating. No novel insight or complex problem-solving 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 |
5 The functions f and g are defined with their respective domains by
$$\begin{array} { l l }
\mathrm { f } ( x ) = \sqrt { 2 x - 5 } , & \text { for } x \geqslant 2.5 \\
\mathrm {~g} ( x ) = \frac { 10 } { x } , & \text { for real values of } x , \quad x \neq 0
\end{array}$$
\begin{enumerate}[label=(\alph*)]
\item State the range of f .
\item \begin{enumerate}[label=(\roman*)]
\item Find $\mathrm { fg } ( x )$.
\item Solve the equation $\operatorname { fg } ( x ) = 5$.
\end{enumerate}\item The inverse of f is $\mathrm { f } ^ { - 1 }$.
\begin{enumerate}[label=(\roman*)]
\item Find $\mathrm { f } ^ { - 1 } ( x )$.
\item Solve the equation $\mathrm { f } ^ { - 1 } ( x ) = 7$.
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{AQA C3 2012 Q5 [10]}}