4400 Higher November 2006 Paper 3 Q17
17 The function f is defined as \(\mathrm{f}(x) = \dfrac{x}{x - 1}\).
(a) Find the value of
(i) \(\mathrm{f}(3)\),
(ii) \(\mathrm{f}(-3)\). (2)
(b) State which value(s) of \(x\) must be excluded from the domain of f. (1)
(c)
(i) Find \(\mathrm{ff}(x)\).
Give your answer in its most simple form.
Give your answer in its most simple form.
(ii) What does your answer to (c)(i) show about the function f? (4)
| Scheme | Marks |
|---|---|
| (i) Answer: \(1\frac{1}{2}\) oe | B1 |
| (ii) Answer: \(\frac{3}{4}\) oe | B1 |
| (2) |
Notes
B1: Don’t accept \(\dfrac{-3}{-4}\)
| Scheme | Marks |
|---|---|
| 1 | B1 |
| (1) |
Notes
B1: cao
| Scheme | Marks |
|---|---|
(i) \(\dfrac{\frac{x}{x - 1}}{\frac{x}{x - 1} - 1}\) | M1 |
| \(\dfrac{\frac{x}{x - 1}}{\frac{x - (x - 1)}{x - 1}}\) or \(\dfrac{x}{x - (x - 1)}\) oe | M1 |
| \(x\) | A1 |
| (ii) Answer: eg f is its own inverse, \(\mathrm{f}^{-1} = \mathrm{f}\) | B1 |
| (4) | |
| (7 marks) |
Notes
A1: cao
B1: dep on correct ci
SC B1 for \(\mathrm{ff}(x)\) evaluated correctly for two values of \(x\) and an answer of \(x\)