| Exam Board | Edexcel |
|---|---|
| Module | AEA (Advanced Extension Award) |
| Year | 2017 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | Solve equation involving composites |
| Difficulty | Standard +0.8 This AEA question requires finding an inverse function, determining a range by completing the square, and solving a composite function equation. While each individual step uses standard techniques, part (c) requires solving √(x²-4x+7) = x, which involves squaring, rearranging a quadratic, and checking validity of solutions—a multi-step problem requiring careful algebraic manipulation beyond routine A-level exercises. |
| 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
$$\mathrm { f } ( x ) = \sqrt { x + 2 } \quad \text { for } \quad x \in \mathbb { R } , x \geqslant 0$$
\begin{enumerate}[label=(\alph*)]
\item Find $\mathrm { f } ^ { - 1 } ( x )$ and state the domain of $\mathrm { f } ^ { - 1 }$
The function g is given by
$$\mathrm { g } ( x ) = x ^ { 2 } - 4 x + 5 \text { for } x \in \mathbb { R } , x \geqslant 0$$
\item Find the range of g .
\item Solve the equation $\operatorname { fg } ( x ) = x$ .
\end{enumerate}
\hfill \mbox{\textit{Edexcel AEA 2017 Q1 [7]}}