Specimen 2020 Paper 2 Q13
13 \(\mathrm{f}(x) = 3x^2 + 6 \qquad\) for all \(x\)
\(\mathrm{g}(x) = \sqrt{x - 5} \qquad x \geqslant 5\)
(a) Work out the value of \(\quad \mathrm{gf}(4)\) [2 marks]
(b) Show that \(\ \mathrm{fg}(x)\ \) can be written in the form \(\quad a(x - a) \quad\) where \(a\) is an integer. [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(3 \times 4^2 + 6\) or \(3 \times 16 + 6\) or 54 or \(\sqrt{3x^2 + 6 - 5}\) or \(\sqrt{3x^2 + 1}\) | M1 | oe |
| 7 | A1 |
| Answer | Mark | Comments |
|---|---|---|
| \(3(x - 5) + 6\) | M1 | oe |
| \(3x - 9 = 3(x - 3)\) | A1 |