| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2024 |
| Session | October |
| Marks | 11 |
| Topic | Composite & Inverse Functions |
| Type | State domain or range |
| Difficulty | Moderate -0.3 This is a straightforward multi-part question on functions covering standard techniques: completing the square for range, understanding inverse existence, function composition, and solving a quadratic inequality. All parts are routine A-level procedures with no novel problem-solving required, making it slightly easier than average but not trivial due to the multiple components. |
| Spec | 1.02g Inequalities: linear and quadratic in single variable1.02v Inverse and composite functions: graphs and conditions for existence |
The functions f and g are defined for all real values of $x$ by
$f(x) = 2x^2 + 6x$ and $g(x) = 3x + 2$.
\begin{enumerate}[label=(\alph*)]
\item Find the range of f. [3]
\item Give a reason why f has no inverse. [1]
\item Given that $fg(-2) = g^{-1}(a)$, where $a$ is a constant, determine the value of $a$. [4]
\item Determine the set of values of $x$ for which $f(x) > g(x)$. Give your answer in set notation. [3]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM 2024 Q4 [11]}}