4400 Higher November 2009 Paper 3 Q24
24 \(\mathrm{f}(x) = x^2\)
\(\mathrm{g}(x) = x - 3\)
(a)
(i) Find \(\mathrm{gf}(x)\)
(ii) Find \(\mathrm{g}^{-1}(x)\) (2)
(b) Solve the equation \(\mathrm{gf}(x) = \mathrm{g}^{-1}(x)\) (3)
| Scheme | Marks |
|---|---|
| (i) Answer: \(x^2 - 3\) | B1 |
| (ii) Answer: \(x + 3\) | B1 |
| (2) |
Notes
B1: accept “\(y\) =” \(x^2 - 3\)
B1: accept “\(y\) =” \(x + 3\)
| Scheme | Marks |
|---|---|
| “\(x^2 - 3\)” = “\(x + 3\)” | M1ft |
| \(x^2 - x - 6 = 0\) \((x - 3)(x + 2)\ (= 0)\) | M1 |
| \(x = 3\) \(\quad x = -2\) | A1 |
| (3) | |
| (5 marks) |
Notes
M1ft: quadratic = linear (\(ax + b\)) \(a, b \ne 0\)
M1: or formula reaching \((x =)\ (1 \pm \sqrt{25})/2\)
A1: cao algebraic method reqd