| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2021 |
| Session | June |
| Marks | 5 |
| Topic | Composite & Inverse Functions |
| Type | Find inverse function |
| Difficulty | Moderate -0.3 This question involves finding an inverse function value (straightforward substitution and algebraic manipulation) and algebraic manipulation to rewrite a rational function in a different form. Both parts are routine A-level techniques requiring careful algebra but no problem-solving insight or novel approaches. The manipulation in part (b) is slightly more involved than typical, preventing this from being significantly below average. |
| Spec | 1.02v Inverse and composite functions: graphs and conditions for existence |
The function $\mathbf{f}$ is defined by
$$\mathbf{f}(x) = \frac{3x - 7}{x - 2} \quad x \in \mathbb{R}, x \neq 2$$
\begin{enumerate}[label=(\alph*)]
\item Find $\mathbf{f}^{-1}(7)$ [2]
\item Show that $\mathbf{f}(x) = \frac{ax + b}{x - 3}$ where $a$ and $b$ are integers to be found. [3]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Pure 2021 Q4 [5]}}