| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2022 |
| Session | February |
| Marks | 9 |
| Topic | Composite & Inverse Functions |
| Type | Find inverse function |
| Difficulty | Moderate -0.8 This is a straightforward question on inverse functions with routine components: (i) direct substitution into a quadratic, (ii) finding an inverse by swapping and rearranging (domain restriction makes this simpler), and (iii) reflecting the graph in y=x. All parts are standard textbook exercises requiring no problem-solving insight, 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 |
The diagram shows the graph of $y = f(x)$, where
$f(x) = 2 - x^2, \quad x \leqslant 0$.
\includegraphics{figure_8}
\begin{enumerate}[label=(\roman*)]
\item Evaluate $f(-3)$. [3]
\item Find an expression for $f^{-1}(x)$. [3]
\item Sketch the graph of $y = f^{-1}(x)$. Indicate the coordinates of the points where the graph meets the axes. [3]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM 2022 Q8 [9]}}