| Exam Board | OCR |
|---|---|
| Module | H240/01 (Pure Mathematics) |
| Year | 2017 |
| Session | Specimen |
| Marks | 9 |
| Topic | Composite & Inverse Functions |
| Type | Find composite function expression |
| Difficulty | Moderate -0.3 This is a straightforward composite function question requiring standard techniques: finding fg(x) by substitution, completing the square to find range, solving a quadratic equation, and checking if a function is one-to-one. All parts are routine A-level procedures with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.02u Functions: definition and vocabulary (domain, range, mapping)1.02v Inverse and composite functions: graphs and conditions for existence |
For all real values of $x$, the functions f and g are defined by $f(x) = x^2 + 8ax + 4a^2$ and $g(x) = 6x - 2a$, where $a$ is a positive constant.
\begin{enumerate}[label=(\alph*)]
\item Find fg$(x)$.
Determine the range of fg$(x)$ in terms of $a$. [4]
\item If fg$(2) = 144$, find the value of $a$. [3]
\item Determine whether the function fg has an inverse. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/01 2017 Q11 [9]}}