Higher June 2017 Paper 1 Q20
20. The functions \(g(x)\) and \(h(x)\) are defined, for \(x \gt 2\), by
\[\begin{aligned} g(x) &= x^2 - 1, \\ h(x) &= 3x. \end{aligned}\](a) Find the value of \(hg(9)\). [2]
(b) Find and simplify an expression for \(gh(2x)\). [3]
| Scheme | Marks | Comments |
|---|---|---|
| \(g(9)\ (= 9^2 - 1) = 80\) | B1 | or for \(hg(x) = 3(x^2 - 1)\) |
| \(h(80) = 240\) or \(hg(9) = 240\) | B1 | FT ‘their \(9^2 - 1\)’ or ‘their \(3(x^2 - 1)\)’ |
| Scheme | Marks | Comments |
|---|---|---|
| \(h(2x) = 3(2x)\) | M1 | or for \(gh(x) = (3x)^2 - 1\) |
| \(gh(2x) = (6x)^2 - 1\) | M1 | FT ‘their \(gh(x)\)’ or ‘their \(h(2x)\)’ |
| \(gh(2x) = 36x^2 - 1\) | A1 | CAO |
| (5) |