| Exam Board | OCR |
|---|---|
| Module | H240/03 (Pure Mathematics and Mechanics) |
| Year | 2020 |
| Session | November |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | State domain or range |
| Difficulty | Moderate -0.8 This is a straightforward multi-part question testing standard A-level techniques: completing the square for range, understanding inverse functions, function composition, and solving a quadratic inequality. All parts are routine applications of core methods with no novel problem-solving required, making it easier than average. |
| Spec | 1.02e Complete the square: quadratic polynomials and turning points1.02g Inequalities: linear and quadratic in single variable1.02h Express solutions: using 'and', 'or', set and interval notation1.02u Functions: definition and vocabulary (domain, range, mapping)1.02v 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{OCR H240/03 2020 Q3 [11]}}