Higher June 2022 Paper 2 Q19
19 The functions g and h are such that
\[\mathrm{g}(x) = \sqrt[3]{2x - 5} \qquad\qquad \mathrm{h}(x) = \frac{1}{x}\](a) Find \(\mathrm{g}(16)\) (1)
(b) Find \(\mathrm{hg}^{-1}(x)\)
Give your answer in terms of \(x\) in its simplest form. (3)
Give your answer in terms of \(x\) in its simplest form. (3)
| Answer | Mark | Mark scheme |
|---|---|---|
| 3 | B1 | cao |
| Answer | Mark | Mark scheme |
|---|---|---|
| \(\dfrac{2}{x^3 + 5}\) | M1 | for finding \(\left(\mathrm{g}^{-1}(x) =\right) \dfrac{x^3 + 5}{2}\) oe |
| M1 | for \(\left(\mathrm{hg}^{-1}(x) =\right) = \dfrac{1}{\left[\mathrm{g}^{-1}(x)\right]}\) oe | |
| A1 | Accept \(\left(\dfrac{x^3 + 5}{2}\right)^{-1}\) |
Additional guidance
[\(\mathrm{g}^{-1}(x)\)] must be their inverse function and cannot be \(\sqrt[3]{2x - 5}\)