| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | Evaluate composite at point |
| Difficulty | Moderate -0.3 This is a straightforward multi-part question on composite and inverse functions requiring routine algebraic manipulation. Part (i) is direct substitution, part (ii) involves solving a simple equation after composing functions, and part (iii) is standard inverse function technique. All parts are mechanical applications of well-practiced procedures with no conceptual challenges, making it slightly easier than the average A-level question. |
| Spec | 1.02u Functions: definition and vocabulary (domain, range, mapping)1.02v Inverse and composite functions: graphs and conditions for existence |
6. The functions $f$ and $g$ are defined by
$$\begin{aligned}
& \mathrm { f } : x \rightarrow 3 x - 4 , \quad x \in \mathbb { R } , \\
& \mathrm {~g} : x \rightarrow \frac { 2 } { x + 3 } , \quad x \in \mathbb { R } , \quad x \neq - 3
\end{aligned}$$
(i) Evaluate fg(1).\\
(ii) Solve the equation $\operatorname { gf } ( x ) = 6$.\\
(iii) Find an expression for $\mathrm { g } ^ { - 1 } ( x )$.\\
\hfill \mbox{\textit{OCR C3 Q6 [8]}}