| Exam Board | Edexcel |
|---|---|
| Module | AEA (Advanced Extension Award) |
| Year | 2012 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | Find range of composite |
| Difficulty | Challenging +1.2 This AEA question requires completing the square to find the range of a quadratic, then composing functions and analyzing the resulting domain/range. While it involves multiple steps and careful tracking of restrictions, the techniques are standard A-level methods without requiring novel insight or proof—moderately above average difficulty due to the composition analysis and AEA context. |
| Spec | 1.02u Functions: definition and vocabulary (domain, range, mapping)1.02v Inverse and composite functions: graphs and conditions for existence |
1.The function f is given by
$$\mathrm { f } ( x ) = x ^ { 2 } - 2 x + 6 , \quad x \geqslant 0$$
\begin{enumerate}[label=(\alph*)]
\item Find the range of $f$ .
The function $g$ is given by
$$\mathrm { g } ( x ) = 3 + \sqrt { } ( x + 4 ) , \quad x \geqslant 2$$
\item Find $\operatorname { gf } ( x )$ .
\item Find the domain and range of gf.
\end{enumerate}
\hfill \mbox{\textit{Edexcel AEA 2012 Q1 [8]}}