| Exam Board | OCR |
|---|---|
| Module | H240/03 (Pure Mathematics and Mechanics) |
| Year | 2022 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | Find inverse function |
| Difficulty | Easy -1.2 This question tests basic transformations and inverse functions with straightforward procedures: identifying a vertical translation, finding the inverse of a simple cubic function by swapping and rearranging, and recalling that inverse functions reflect in y=x. All parts are routine recall and standard techniques with no problem-solving required, making it easier than average. |
| Spec | 1.02v Inverse and composite functions: graphs and conditions for existence1.02w Graph transformations: simple transformations of f(x) |
\begin{enumerate}[label=(\alph*)]
\item Give full details of the single transformation that transforms the graph of $y = x^3$ to the graph of $y = x^3 - 8$. [2]
\end{enumerate}
The function f is defined by $\mathrm{f}(x) = x^3 - 8$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find an expression for $\mathrm{f}^{-1}(x)$. [2]
\item State how the graphs of $y = \mathrm{f}(x)$ and $y = \mathrm{f}^{-1}(x)$ are related geometrically. [1]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/03 2022 Q2 [5]}}