Higher June 2022 Paper 1 Q20
20.
\[g(x) = \dfrac{x}{2}\]\[h(x) = x^3\](a) Find \(hg\left(\dfrac{1}{3}\right)\). [2]
(b) Solve \(h^{-1}(x) = -2\). [2]
| Scheme | Marks | Comments |
|---|---|---|
| \(h\left(\dfrac{1}{6}\right)\) or \(\left(\dfrac{1}{6}\right)^3\) OR \(hg(x) = \dfrac{x^3}{8}\) oe | M1 | must be \(\dfrac{1}{6}\) OR Accept e.g. \(hg(x) = \left(\dfrac{x}{2}\right)^3\) Allow e.g. \(hg \to \left(\dfrac{x}{2}\right)^3\) or any clear indication they know what the function is |
| \(\dfrac{1}{216}\) | A1 | If no marks, SC1 for ‘their \(\dfrac{\dfrac{1}{3}}{2}\)’ correctly cubed, as final answer providing they have shown \(\dfrac{\dfrac{1}{3}}{2}\) or exact equivalent |
| Scheme | Marks | Comments |
|---|---|---|
| \(h^{-1}(x) = \sqrt[3]{x}\) or \(x = h(-2)\) or \((-2)^3\) | M1 | |
| \((x =)\ -8\) | A1 | |
| (4) |