| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2024 |
| Session | June |
| Marks | 6 |
| Topic | Composite & Inverse Functions |
| Type | Find inverse function |
| Difficulty | Moderate -0.8 This is a straightforward multi-part question on standard function operations. Part (a) requires identifying the range of a quadratic with restricted domain (routine), part (b) is direct substitution into a composite function, and part (c) involves finding an inverse of a simple rational function using the standard method (swap x and y, rearrange). All parts are textbook exercises requiring only procedural knowledge with no problem-solving or novel insight. |
| Spec | 1.02u Functions: definition and vocabulary (domain, range, mapping)1.02v Inverse and composite functions: graphs and conditions for existence |
\begin{enumerate}
\item The functions $f$ and $g$ are defined by
\end{enumerate}
$$\begin{array} { l l l }
\mathrm { f } ( x ) = 9 - x ^ { 2 } & x \in \mathbb { R } & x \geq 0 \\
\mathrm {~g} ( x ) = \frac { 3 } { 2 x + 1 } & x \in \mathbb { R } & x \geq 0
\end{array}$$
(a) Write down the range of f\\
(b) Find the value of fg (1.5)\\
(c) Find $\mathrm { g } ^ { - 1 } ( x )$ and state the domain of $\mathrm { g } ^ { - 1 } ( x )$\\
\hfill \mbox{\textit{SPS SPS SM Pure 2024 Q1 [6]}}