| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2024 |
| Session | September |
| Marks | 5 |
| Topic | Composite & Inverse Functions |
| Type | Find inverse function |
| Difficulty | Moderate -0.3 This is a straightforward inverse function question with standard techniques. Part (a) requires simple function composition (substituting f(6) into f), and part (b) involves the routine algebraic manipulation of swapping x and y to find the inverse of a rational function. The domain statement is a direct consequence of the original function's range. This is slightly easier than average as it's a textbook exercise with no conceptual challenges. |
| 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 function f is defined by
\end{enumerate}
$$\mathrm { f } ( x ) = \frac { x + 3 } { x - 4 } \quad x \in \mathbb { R } , x \neq 4$$
(a) Find ff (6)\\
(2)\\
(b) Find $\mathrm { f } ^ { - 1 }$ and state its domain\\
(3)
\section*{(Total for Question 3 is 5 marks)}
\hfill \mbox{\textit{SPS SPS SM Pure 2024 Q3 [5]}}