| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2024 |
| Session | October |
| Marks | 8 |
| Topic | Composite & Inverse Functions |
| Type | Find inverse function |
| Difficulty | Standard +0.3 This is a straightforward inverse function question requiring standard techniques: swap x and y, apply inverse operations (ln then arcsin), and determine domain from the range of g(x). The degree notation and sketching add minor complexity, but the algebraic manipulation is routine for A-level Further Maths students. |
| Spec | 1.02v Inverse and composite functions: graphs and conditions for existence1.05a Sine, cosine, tangent: definitions for all arguments1.06a Exponential function: a^x and e^x graphs and properties |
3. The function $g ( x )$ is defined as follows:
$$g ( x ) = e ^ { \sin \left( x ^ { \circ } \right) } , - 90 \leq x \leq 90$$
\begin{enumerate}[label=(\alph*)]
\item Find $g ^ { - 1 } ( x )$, stating its domain.
\item Sketch $y = g ^ { - 1 } ( x )$ on the axes provided below, being sure to label all key points.\\
\includegraphics[max width=\textwidth, alt={}, center]{4c649001-3816-4cfa-9418-e3e427df1eb5-07_1524_1591_459_342}
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM 2024 Q3 [8]}}