Higher June 2025 Paper 2R Q19
19 The functions f and g are such that
\[\begin{aligned} \mathrm{f}(x) &= 3x - 4 \quad \text{where } x \gt 2 \\ \mathrm{g}(x) &= \dfrac{x}{2x + 1} \end{aligned}\](a) State the value of \(x\) that cannot be included in any domain of g (1)
(b) Find \(\mathrm{gf}(x)\)
Give your answer in its simplest form. (2)
Give your answer in its simplest form. (2)
| Scheme | Marks |
|---|---|
| \(-\dfrac{1}{2}\) | B1 |
| (1) |
Notes
B1: oe
Accept \(x = -\dfrac{1}{2}\), accept \(x \ne -\dfrac{1}{2}\)
Do not allow inequalities, eg \(x \gt -\dfrac{1}{2}\) or \(x \leqslant -\dfrac{1}{2}\)
| Scheme | Marks |
|---|---|
| \(\dfrac{3x - 4}{2(3x - 4) + 1}\) | M1 |
Correct answer only scores full marks (unless from obviously incorrect working) Answer: \(\dfrac{3x - 4}{6x - 7}\) | A1 |
| (2) | |
| (3 marks) |
Notes
M1: for a correct unsimplified expression for \(\mathrm{gf}(x)\)
A1: oe eg \(\dfrac{4 - 3x}{7 - 6x}\)
Correct answer seen followed by incorrect subsequent working scores M1A0