| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2021 |
| Session | May |
| Marks | 7 |
| Topic | Composite & Inverse Functions |
| Type | Find inverse function |
| Difficulty | Moderate -0.8 This is a straightforward functions question requiring basic evaluation of a square root, finding an inverse by swapping and rearranging (one-step algebra), and sketching reflection in y=x. All parts are routine procedures with no problem-solving or conceptual challenge, making it easier than the average A-level question. |
| Spec | 1.02u Functions: definition and vocabulary (domain, range, mapping)1.02v Inverse and composite functions: graphs and conditions for existence |
The function f is defined for all non-negative values of $x$ by
$$f(x) = 3 + \sqrt{x}.$$
\begin{enumerate}[label=(\roman*)]
\item Evaluate $f(169)$. [2]
\item Find an expression for $f^{-1}(x)$ in terms of $x$. [2]
\item On a single diagram sketch the graphs of $y = f(x)$ and $y = f^{-1}(x)$, indicating how the two graphs are related. [3]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Pure 2021 Q1 [7]}}