| Exam Board | WJEC |
|---|---|
| Module | Unit 3 (Unit 3) |
| Year | 2024 |
| Session | June |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | Find inverse function |
| Difficulty | Standard +0.3 This is a structured multi-part question on rational functions requiring algebraic manipulation (partial fractions in reverse), range determination from a restricted domain, finding an inverse function, and solving f(x)=f^{-1}(x). While it involves several techniques, each part follows standard A-level procedures with clear scaffolding. The algebra is moderately involved but routine for C3 level, making it slightly easier than average overall. |
| Spec | 1.02k Simplify rational expressions: factorising, cancelling, algebraic division1.02v Inverse and composite functions: graphs and conditions for existence |
The function $f$ has domain $[4, \infty)$ and is defined by
$$f(x) = \frac{2(3x + 1)}{x^2 - 2x - 3} + \frac{x}{x + 1}.$$
\begin{enumerate}[label=(\alph*)]
\item Show that $f(x) = \frac{x + 2}{x - 3}$. [4]
\item Determine the range of $f(x)$. [2]
\item Find an expression for $f^{-1}(x)$ and write down the domain and range of $f^{-1}$. [4]
\item Find the value of $x$ when $f(x) = f^{-1}(x)$. [4]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 3 2024 Q10 [14]}}