| Exam Board | Edexcel |
|---|---|
| Module | AEA (Advanced Extension Award) |
| Year | 2016 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | Find range of composite |
| Difficulty | Standard +0.8 This AEA question requires completing the square to find f's range, then composing functions and analyzing the composite's domain/range. While it involves multiple steps and careful domain tracking, the techniques are standard A-level methods applied systematically rather than requiring novel insight or proof. |
| 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
$$\mathrm { f } ( x ) = x ^ { 2 } - 4 x + 9 \quad x \in \mathbb { R } , x \geqslant 3$$
\begin{enumerate}[label=(\alph*)]
\item Find the range of f .
The function g is given by
$$\operatorname { g } ( x ) = \frac { 10 } { x + 1 } \quad x \in \mathbb { R } , x \geqslant 4$$
\item Find an expression for $\operatorname { gf } ( x )$ .
\item Find the domain and range of gf.
\end{enumerate}
\hfill \mbox{\textit{Edexcel AEA 2016 Q1 [7]}}