| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | Solve equation involving composites |
| Difficulty | Moderate -0.3 This is a straightforward composite functions question with standard techniques: completing the square for range, direct substitution for composition evaluation, and solving a simple quadratic equation. All parts are routine C3 exercises requiring no novel insight, making it slightly easier than average. |
| Spec | 1.02e Complete the square: quadratic polynomials and turning points1.02v Inverse and composite functions: graphs and conditions for existence |
5. The functions $f$ and $g$ are defined by
$$\begin{aligned}
& \mathrm { f } ( x ) \equiv x ^ { 2 } - 3 x + 7 , \quad x \in \mathbb { R } , \\
& \mathrm {~g} ( x ) \equiv 2 x - 1 , \quad x \in \mathbb { R } .
\end{aligned}$$
(i) Find the range of f .\\
(ii) Evaluate $g f ( - 1 )$.\\
(iii) Solve the equation
$$\operatorname { fg } ( x ) = 17$$
\hfill \mbox{\textit{OCR C3 Q5 [9]}}