| Exam Board | OCR |
|---|---|
| Module | H240/01 (Pure Mathematics) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | Find composite function expression |
| Difficulty | Moderate -0.3 This is a straightforward composite function question requiring algebraic substitution and completing the square to find the range. Part (a) involves routine substitution and simplification, part (b) is simple equation solving, and part (c) requires recognizing that a quadratic (parabola) fails the horizontal line test. All techniques are standard 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 |
11 For all real values of $x$, the functions f and g are defined by $\mathrm { f } ( x ) = x ^ { 2 } + 8 a x + 4 a ^ { 2 }$ and $g ( x ) = 6 x - 2 a$, where $a$ is a positive constant.
\begin{enumerate}[label=(\alph*)]
\item Find $\mathrm { fg } ( x )$.
Determine the range of $\mathrm { fg } ( x )$ in terms of $a$.
\item If $f g ( 2 ) = 144$, find the value of $a$.
\item Determine whether the function fg has an inverse.
\end{enumerate}
\hfill \mbox{\textit{OCR H240/01 Q11 [9]}}