4400 Higher November 2004 Paper 4 Q22
22
\[\mathrm{f}(x) = x^2\] \[\mathrm{g}(x) = x - 6\]Solve the equation \(\mathrm{fg}(x) = \mathrm{g}^{-1}(x)\)
(5)
| Scheme | Marks |
|---|---|
| \((x - 6)^2 = x + 6\) | B1 B1 |
| \(x^2 - 12x + 36 = x + 6\) \(x^2 - 13x + 30 = 0\) | M1 |
| \((x - 10)(x - 3) = 0\) | M1 |
| \(x = 10\) or \(x = 3\) | A1 |
| (5) | |
| (5 marks) |
Notes
B1: for \((x - 6)^2\)
B1: for \(x + 6\)
M1: for \(x^2 - 13x + 30 = 0\)
M1: for \((x - 10)(x - 3) = 0\)
A1: cao