| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | Evaluate composite at point |
| Difficulty | Standard +0.3 This is a straightforward composite/inverse functions question requiring completion of the square to find a range and simple substitution to find a constant. Both parts use standard C3 techniques with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.02e Complete the square: quadratic polynomials and turning points1.02u Functions: definition and vocabulary (domain, range, mapping) |
The functions $f$ and $g$ are defined by
$$f: x \mapsto x^2 - 2x + 3, x \in \mathbb{R}, \quad 0 \leq x \leq 4,$$
$$g: x \mapsto \lambda x^2 + 1, \text{ where } \lambda \text{ is a constant, } x \in \mathbb{R}.$$
\begin{enumerate}[label=(\alph*)]
\item Find the range of $f$. [3]
\item Given that $gf(2) = 16$, find the value of $\lambda$. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C3 Q26 [6]}}