Higher November 2023 Paper 2 Q19
19 The functions f and g are such that
\[\text{f}(x) = (2x + 3)^2 \quad \text{and} \quad \text{g}(x) = 2x - 1\](a) Find \(\text{gf}(-3)\) (2)
(b) Find \(\text{g}^{-1}(x)\) (2)
| Answer | Mark | Mark scheme |
|---|---|---|
| 17 | M1 | For \((\text{gf}(x) =)\ 2(2x + 3)^2 - 1\) or \((\text{gf}(x) =)\ 8x^2 + 24x + 17\) or \(2(2 \times (-3) + 3)^2 - 1\) |
| A1 | cao |
Additional guidance
Substitution may be seen in 2 steps
| Answer | Mark | Mark scheme |
|---|---|---|
| \(\dfrac{x + 1}{2}\) | M1 | for a suitable first step, eg adds 1 to both sides, eg \(y + 1 = 2x\) or \(x + 1 = 2y\) or \(\text{g}(x) + 1 = 2x\) or \(x = \dfrac{y + 1}{2}\) |
| A1 | oe |