Higher June 2024 Paper 3 Q16
16 The functions f and g are given by
\[\text{f}(x) = \dfrac{12}{x + 1} \quad \text{and} \quad \text{g}(x) = 5 - 3x\](a) Find \(\text{f}(-3)\) (1)
(b) Find \(\text{fg}(1)\) (2)
(c) Find \(\text{g}^{-1}(4)\) (2)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(-6\) | B1 | cao |
| Answer | Mark | Mark scheme |
|---|---|---|
| 4 | M1 | for \(\text{g}(1) = 5 - 3 \times 1\ (= 2)\) and a clear intention to find \(\text{f}(\text{``}2\text{''})\) or for \(\dfrac{12}{5 - 3 \times 1 + 1}\) or for stating fg, eg \(\dfrac{12}{5 - 3x + 1}\) oe |
| A1 | cao |
Additional guidance
For reference
\(\text{f}(x) = \dfrac{12}{x + 1}\) and \(\text{g}(x) = 5 - 3x\)
Accept \(\dfrac{4}{1}\)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(\dfrac{1}{3}\) | M1 | for \(\text{g}^{-1}\) as \(\dfrac{5 - x}{3}\) oe or for \(5 - 3x = 4\) or \(\text{g}\left(\dfrac{1}{3}\right) = 5 - 1 = 4\) |
| A1 | for \(\dfrac{1}{3}\) oe eg 0.33(3…) |
Additional guidance
Could be shown in the form of a flowchart, which must show correct inverse operations.
Allow \(\text{g}^{-1}\) and g to be in terms of \(y\)
ie accept \(\dfrac{5 - y}{3}\) and \(5 - 3y = 4\)