Higher January 2019 Paper 1 Q19
19 g is the function with domain \(x \geqslant -3\) such that \(\text{g}(x) = x^2 + 6x\)
(a) Write down the range of \(\text{g}^{-1}\) (1)
(b) Express the inverse function \(\text{g}^{-1}\) in the form \(\text{g}^{-1} : x \mapsto \ldots\) (4)
| Scheme | Marks |
|---|---|
| \(y \geqslant -3\) | B1 |
| (1) |
Notes
B1: Accept \(\text{g}^{-1}(x) \geqslant -3\)
| Scheme | Marks |
|---|---|
| \((x + 3)^2 - 3^2\) or \((x + 3)^2 - 9\) or \((y + 3)^2 - 3^2\) or \((y + 3)^2 - 9\) | M1 |
| \(y + 9 = (x + 3)^2\) or \(x + 9 = (y + 3)^2\) | M1 |
| \(\sqrt{y + 9} = x + 3\) or \(\sqrt{x + 9} = y + 3\) | M1 |
| \(-3 + \sqrt{x + 9}\) | A1 |
| (4) | |
| (5 marks) |
Notes
M1: for completing the square
A1: oe
M3A0 for \(-3 + \sqrt{y + 9}\) and for \(-3 \pm \sqrt{x + 9}\)