| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | Find composite function expression |
| Difficulty | Standard +0.3 This is a standard C3 question on functions covering range, inverse functions, graph sketching, and composite functions. Parts (a)-(c) require routine completion of the square and understanding of inverse function properties. Parts (d)-(e) involve straightforward function composition and solving a modulus equation. While multi-part with 14 marks total, each component uses well-practiced techniques without requiring novel insight, making it slightly easier than the typical average A-level question. |
| Spec | 1.02e Complete the square: quadratic polynomials and turning points1.02l Modulus function: notation, relations, equations and inequalities1.02v Inverse and composite functions: graphs and conditions for existence |
f(x) = $x^2 - 2x - 3$, $x \in \mathbb{R}$, $x \geq 1$.
\begin{enumerate}[label=(\alph*)]
\item Find the range of f. [1]
\item Write down the domain and range of $f^{-1}$. [2]
\item Sketch the graph of $f^{-1}$, indicating clearly the coordinates of any point at which the graph intersects the coordinate axes. [4]
\end{enumerate}
Given that g(x) = $|x - 4|$, $x \in \mathbb{R}$,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{3}
\item find an expression for gf(x). [2]
\item Solve gf(x) = 8. [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C3 Q6 [14]}}