4MA0 Higher June 2013 Paper 4R Q23
23
(a) Show that \(\dfrac{x^2 + 3x}{2x^2 + 5x - 3}\) can be written as \(\dfrac{x}{kx - 1}\)
State the value of \(k\). (2)
State the value of \(k\). (2)
(b) \(\mathrm{f}(x) = \dfrac{x}{2x - 1}\)
Find the inverse function \(\mathrm{f}^{-1}\) in the form \(\mathrm{f}^{-1}(x) = \ldots\ldots\)
Show your working clearly. (3)
Find the inverse function \(\mathrm{f}^{-1}\) in the form \(\mathrm{f}^{-1}(x) = \ldots\ldots\)
Show your working clearly. (3)
| Scheme | Marks |
|---|---|
| \(\dfrac{x(x+3)}{(2x-1)(x+3)}\) | M1 |
| 2 | A1 |
| (2) |
Notes
M1: for factorising numerator and denominator
A1: cao dep on method mark
| Scheme | Marks |
|---|---|
| \(y = \dfrac{x}{2x - 1}\) | M1 |
| \(2xy - x = y\) or \(x(2y - 1) = y\) | M1 |
| \(\dfrac{x}{2x - 1}\) | A1 |
| (3) |
Notes
M1: for isolating \(x\) terms (or \(y\) terms in alt method)
A1: dep on both method marks.
Accept \(\dfrac{-x}{-2x + 1}\)
Alternative method
\(x = \dfrac{y}{2y - 1}\)
\(2xy - y = x\) or \(y(2x - 1) = x\)