Higher November 2024 Paper 1 Q18
18 \(\mathrm{f}(x) = \dfrac{5x - 3}{4}\)
(a) Find \(\mathrm{f}^{-1}(x)\) (2)
For all values of \(x\)
\(\mathrm{g}(x) = (x - 1)^2\) and \(\mathrm{h}(x) = 1 - 2x\)
(b) Work out the value of \(\mathrm{gh}(5)\) (2)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(\dfrac{4x + 3}{5}\) | M1 | for first step to change the subject of \(y = \dfrac{5x - 3}{4}\) or \(x = \dfrac{5y - 3}{4}\) eg \(4y = 5x - 3\) or \(4x = 5y - 3\) |
| A1 | oe |
Additional guidance
Answer of \(\dfrac{4y + 3}{5}\) gets M1A0
| Answer | Mark | Mark scheme |
|---|---|---|
| 100 | M1 | for \(\mathrm{h}(5) = 1 - 2 \times 5\ (= -9)\) and a clear intention to find \(\mathrm{g}(\text{``}{-}9\text{''})\) or for \(((1 - 2 \times 5) - 1)^2\) or for stating \(\mathrm{gh}(x)\), eg \((1 - 2x - 1)^2\) oe |
| A1 | cao |