Higher November 2018 Paper 1 Q19
19 For all values of \(x\)
\(\mathrm{f}(x) = (x + 1)^2\) and \(\mathrm{g}(x) = 2(x - 1)\)
(a) Show that \(\mathrm{gf}(x) = 2x(x + 2)\) (2)
(b) Find \(\mathrm{g}^{-1}(7)\) (2)
| Answer | Mark | Mark scheme |
|---|---|---|
| shown | C1 | for first step, eg \(2((x + 1)^2 - 1)\) or \(2(x^2 + 2x + 1 - 1)\) oe |
| C1 | for fully correct chain of reasoning |
Additional guidance
It is insufficient to state \(\mathrm{gf}(x) = 2x(x + 2)\) without showing the first step, and the following sequence of algebraic steps leading to it.
| Answer | Mark | Mark scheme |
|---|---|---|
| 4.5 | M1 | process to find inverse of g, eg \(g^{-1}(x) = \dfrac{1}{2}x + 1\) or for \(2(x - 1) = 7\) |
| A1 | for 4.5 oe |
Additional guidance
Could be shown in the form of a flowchart, which must show inverse operations.