| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | Solve equation involving composites |
| Difficulty | Standard +0.3 This is a straightforward composite function question requiring evaluation of fg(2) by substituting g(2) into f, then solving gf(x)=1/2 by composing the functions and solving a quadratic equation. All steps are routine C3 techniques with no novel insight required, making it slightly easier than average. |
| Spec | 1.02f Solve quadratic equations: including in a function of unknown1.02u Functions: definition and vocabulary (domain, range, mapping)1.02v Inverse and composite functions: graphs and conditions for existence |
2. The functions $f$ and $g$ are defined by
$$\begin{aligned}
& f : x \rightarrow 2 - x ^ { 2 } , \quad x \in \mathbb { R } , \\
& g : x \rightarrow \frac { 3 x } { 2 x - 1 } , \quad x \in \mathbb { R } , \quad x \neq \frac { 1 } { 2 } .
\end{aligned}$$
(i) Evaluate fg(2).\\
(ii) Solve the equation $\operatorname { gf } ( x ) = \frac { 1 } { 2 }$.\\
\hfill \mbox{\textit{OCR C3 Q2 [6]}}