| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | Find inverse function |
| Difficulty | Moderate -0.3 This is a straightforward inverse function question requiring algebraic manipulation to combine fractions, standard inverse function technique (swap x and y, then solve), and identifying the domain from the range of f. All steps are routine C3 procedures with no conceptual challenges, making it slightly easier than average. |
| Spec | 1.02k Simplify rational expressions: factorising, cancelling, algebraic division1.02v Inverse and composite functions: graphs and conditions for existence |
The function $f$ is given by $f: x \mapsto 2 + \frac{3}{x + 2}, x \in \mathbb{R}, x \neq -2$.
\begin{enumerate}[label=(\alph*)]
\item Express $2 + \frac{3}{x + 2}$ as a single fraction. [1]
\item Find an expression for $f^{-1}(x)$. [3]
\item Write down the domain of $f^{-1}$. [1]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C3 Q33 [5]}}