| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | Find inverse function |
| Difficulty | Moderate -0.3 This is a straightforward C3 inverse function question with routine algebraic manipulation. Part (a) is trivial fraction work, part (b) follows the standard algorithm for finding inverses (swap x and y, rearrange), and part (c) requires recognizing that the domain of f^{-1} equals the range of f. Slightly easier than average due to the simple rational function form and standard procedure. |
| 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 Q2 [5]}}