| Exam Board | WJEC |
|---|---|
| Module | Unit 3 (Unit 3) |
| Year | 2023 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | Find inverse function |
| Difficulty | Moderate -0.8 This is a straightforward function composition and inverse question requiring only routine techniques. Part (a)(i) is direct substitution, part (a)(ii) requires setting the denominator to zero (a standard check), and part (b) is a standard inverse function calculation using algebraic manipulation. All steps are textbook exercises with no problem-solving insight required, making this easier than average. |
| Spec | 1.02u Functions: definition and vocabulary (domain, range, mapping)1.02v Inverse and composite functions: graphs and conditions for existence |
Two real functions are defined as
$$f(x) = \frac{8}{x-4} \quad \text{for} \quad (-\infty < x < 4) \cup (4 < x < \infty),$$
$$g(x) = (x-2)^2 \quad \text{for} \quad -\infty < x < \infty.$$
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Find an expression for $fg(x)$. [2]
\item Determine the values of $x$ for which $fg(x)$ does not exist. [3]
\end{enumerate}
\item Find an expression for $f^{-1}(x)$. [3]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 3 2023 Q10 [8]}}