4MA0 Higher January 2016 Paper 3R Q16
16
\[\mathrm{f}(x) = \frac{2x}{x - 1}\](a) Find the value of f(11) (1)
(b) State which value of \(x\) must be excluded from any domain of f (1)
(c) Find \(\mathrm{f}^{-1}(x)\) (3)
(d) State the value which cannot be in any range of f (1)
| Scheme | Marks |
|---|---|
| 2.2 | B1 |
| (1) |
Notes
B1: Accept \(\dfrac{22}{10}\), \(\dfrac{11}{5}\), \(2\dfrac{1}{5}\)
| Scheme | Marks |
|---|---|
| 1 | B1 |
| (1) |
| Scheme | Marks |
|---|---|
| \(y(x - 1) = 2x\) or \(yx - y = 2x\) or \(x(y - 1) = 2y\) or \(xy - x = 2y\) | M1 |
| \(x(y - 2) = y\) or \(y(x - 2) = x\) | M1 |
| \(\dfrac{x}{x - 2}\) | A1 |
| (3) |
Notes
A1: oe Eg \(\dfrac{-x}{2 - x}\)
M2A0 for \(\dfrac{y}{y - 2}\)
| Scheme | Marks |
|---|---|
| 2 | B1 |
| (1) |
Notes
B1: ft from (c) if a rational function with a linear denominator