4MA0 Higher June 2012 Paper 4 Q19
19 \[\begin{aligned} \mathrm{f}(x) &= 3x - 2 \\ \mathrm{g}(x) &= \dfrac{10}{x + 2} \end{aligned}\]
(a) Express the inverse function \(\mathrm{f}^{-1}\) in the form \(\mathrm{f}^{-1}(x) = ...\) (2)
(b) Find \(\mathrm{gf}(x)\)
Simplify your answer. (2)
Simplify your answer. (2)
| Scheme | Marks |
|---|---|
| \(y = 3x - 2\) \(y + 2 = 3x\) | M1 |
| \((x + 2)/3\) | A1 |
| (2) |
Notes
M1: or \(x = 3y - 2\)
or \(x + 2 = 3y\) must reach 2nd stage
A1: Ans only = M1A1 must be a function of \(x\)
Apart from questions 5, 7, 13c, 16b, 20, 21 and 22 (where the mark scheme states otherwise) the correct answer, unless clearly obtained by an incorrect method, should be taken to imply a correct method.
| Scheme | Marks |
|---|---|
| \(\dfrac{10}{3x - 2 + 2}\) | M1 |
| \(\dfrac{10}{3x}\) | A1 cao |
| (2) | |
| (Total 4 marks) |
Notes
A1 cao: Do not isw if correct answer is seen in body and extra incorrect operations take place. Ans only = M1A1