| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | Find inverse function |
| Difficulty | Moderate -0.3 This is a straightforward multi-part question testing standard C3 techniques: algebraic simplification of rational expressions, finding range from a simplified form, finding an inverse function, and recognizing domain-range relationships. All parts follow routine procedures with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.02k Simplify rational expressions: factorising, cancelling, algebraic division1.02u Functions: definition and vocabulary (domain, range, mapping)1.02v Inverse and composite functions: graphs and conditions for existence |
$$f(x) = \frac{2}{x-1} - \frac{6}{(x-1)(2x+1)}, \quad x > 1.$$
\begin{enumerate}[label=(\alph*)]
\item Prove that $f(x) = \frac{4}{2x+1}$. [4]
\item Find the range of $f$. [2]
\item Find $f^{-1}(x)$. [3]
\item Find the range of $f^{-1}(x)$. [1]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C3 Q10 [10]}}