| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | Evaluate composite at point |
| Difficulty | Moderate -0.3 Part (a) requires completing the square and evaluating endpoints to find the range—a standard C3 technique. Part (b) involves straightforward function composition and solving a linear equation. Both parts are routine exercises with clear methods, making this slightly easier than the average A-level question which typically requires more problem-solving or integration of multiple concepts. |
| Spec | 1.02e Complete the square: quadratic polynomials and turning points1.02n Sketch curves: simple equations including polynomials1.02v Inverse and composite functions: graphs and conditions for existence |
The functions f and g are defined by
$\text{f: } x \mapsto x^2 - 2x + 3, x \in \mathbb{R}, 0 \leq x \leq 4,$
$\text{g: } x \mapsto \lambda x^2 + 1, \text{ where } \lambda \text{ is a constant, } x \in \mathbb{R}.$
\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 Q3 [6]}}