Higher November 2017 Paper 2 Q22
22 The functions f and g are such that
\(\mathrm{f}(x) = 5x + 3 \qquad \mathrm{g}(x) = ax + b \qquad\) where \(a\) and \(b\) are constants.
\(\mathrm{g}(3) = 20\quad\) and \(\quad\mathrm{f}^{-1}(33) = \mathrm{g}(1)\)
Find the value of \(a\) and the value of \(b\). (5)
| Answer | Mark | Notes |
|---|---|---|
| 7, \(-1\) | P1 | for strategy to use \(\mathrm{g}(3) = 20\), e.g. \(3a + b = 20\) |
| P1 | for \(\mathrm{g}(1) = a + b\) | |
| P1 | for a process to find inverse of f. e.g. \(\mathrm{f}^{-1}(x) = \dfrac{x - 3}{5}\) or \(\mathrm{f}^{-1}(33) = 6\) | |
| P1 | for using \(\mathrm{f}^{-1}(33) = \mathrm{g}(1)\) to find an equation e.g. \(\dfrac{33 - 3}{5} = a + b\) | |
| A1 | for \(a = 7\), \(b = -1\) |