| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | Find composite function expression |
| Difficulty | Standard +0.3 This is a standard C3 inverse function question with routine techniques: completing the square to find range, stating domain/range of inverse, sketching (reflection in y=x), and solving a composite function equation. All parts follow predictable patterns with no novel insight required, making it slightly easier than the average A-level question. |
| Spec | 1.02d Quadratic functions: graphs and discriminant conditions1.02l Modulus function: notation, relations, equations and inequalities1.02v Inverse and composite functions: graphs and conditions for existence |
$$f(x) = x^2 - 2x - 3, \quad x \in \mathbb{R}, x \geq 1.$$
\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 Q14 [14]}}