4MA0 Higher January 2015 Paper 3R Q21
21 The functions g and h are defined as
\[\mathrm{g}(x) = \dfrac{x}{2x - 5}\] \[\mathrm{h}(x) = x + 4\](a) Find the value of \(\mathrm{g}(1)\) (1)
(b) State which value of \(x\) must be excluded from any domain of g (1)
(c) Find \(\mathrm{gh}(x)\)
Simplify your answer. (2)
Simplify your answer. (2)
(d) Express the inverse function \(\mathrm{g}^{-1}\) in the form \(\mathrm{g}^{-1}(x) = \ldots\) (3)
| Scheme | Marks |
|---|---|
| \(-\dfrac{1}{3}\) | B1 |
| (1) |
| Scheme | Marks |
|---|---|
| 2.5 oe | B1 |
| (1) |
| Scheme | Marks |
|---|---|
| \(\dfrac{x + 4}{2(x + 4) - 5}\) | M1 |
| \(\dfrac{x + 4}{2x + 3}\) | A1 |
| (2) |
| Scheme | Marks |
|---|---|
| \(y(2x - 5) = x\) | M1 |
| \(2xy - x = 5y\) | M1 |
| \(\dfrac{5x}{2x - 1}\) | A1 |
| (3) | |
| (7 marks) |
Notes
M1: or \(2xy - 5y = x\)
or
or \(x(2y - 5) = y\) oe
M1: or \(x(2y - 1) = 5y\)
or
or \(2xy - y = 5x\) oe
A1: \(\dfrac{5y}{2y - 1}\) is M2 only