| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | Find inverse function |
| Difficulty | Moderate -0.3 This is a straightforward multi-part question testing algebraic manipulation of rational functions and inverse functions. Part (a) requires routine algebraic simplification with common denominators, parts (b-d) are standard bookwork on ranges and inverses. The constraint x > 1 guides the analysis. All techniques are standard C3 material with no novel problem-solving required, 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 |
$$f(x) = \frac{2}{x - 1} - \frac{6}{(x - 1)(2x + 1)}, \quad x > 1$$
\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 Q7 [10]}}