4MA0 Higher January 2017 Paper 3R Q19
19 The function f is defined as \(\;\mathrm{f}(x) = \dfrac{3}{2 - x}\)
(a) State the value of \(x\) which cannot be included in any domain of f. (1)
(b) Find f(–4) (1)
(c) Express the inverse function \(\mathrm{f}^{-1}\) in the form \(\mathrm{f}^{-1}(x) = \ldots\) (2)
The function g is defined as \(\;\mathrm{g}(x) = \dfrac{2x + 1}{3}\)
(d) Express the function fg in the form \(\mathrm{fg}(x) = \ldots\)
Simplify your answer. (2)
Simplify your answer. (2)
| Scheme | Marks |
|---|---|
| 2 | B1 |
| (1) |
| Scheme | Marks |
|---|---|
| 0.5 oe | B1 |
| (1) |
| Scheme | Marks |
|---|---|
| \(y(2 - x) = 3\) or \(x(2 - y) = 3\) oe | M1 |
| \(\dfrac{2x - 3}{x}\) | A1 |
| (2) |
Notes
A1: \(\dfrac{3 - 2x}{-x}\) or \(2 - \dfrac{3}{x}\)
must be in terms of \(x\)
| Scheme | Marks |
|---|---|
| \(\dfrac{3}{2 - \dfrac{2x + 1}{3}}\) oe | M1 |
| \(\dfrac{9}{5 - 2x}\) | A1 |
| (2) | |
| (6 marks) |