4400 Higher November 2007 Paper 4 Q23
23
\[\mathrm{f}: x \mapsto 3x + 2 \qquad \mathrm{g}: x \mapsto 2x - 5\](a) Express the composite function fg in the form \(\mathrm{fg}: x \mapsto \ldots\)
Give your answer as simply as possible. (2)
Give your answer as simply as possible. (2)
(b) Express the inverse function \(\mathrm{f}^{-1}\) in the form \(\mathrm{f}^{-1}: x \mapsto \ldots\) (2)
| Scheme | Marks |
|---|---|
| \(3(2x - 5) + 2\) or \(6x - 15 + 2\) | M1 |
| \(6x - 13\) | A1 |
| (2) |
| Scheme | Marks |
|---|---|
| eg \(\begin{matrix} \times 3 \to +2 \\ \div 3 \leftarrow -2 \end{matrix}\) or attempt to make \(x\) the subject of \(y = 3x + 2\) or \(x = 3y + 2\) | M1 |
| \(\dfrac{x - 2}{3}\) oe | A1 |
| (2) | |
| (4 marks) |