# How do you find the domain and range of (5x+3)/(1-2x)?

Jun 22, 2016

The domain is $\mathbb{R} - \left(\frac{1}{2}\right)$ and the range is $\mathbb{R} - \left(- \frac{5}{2}\right)$

#### Explanation:

the domain is obtained by finding the values for x so that:

1-2x!=0`

or

$x \ne \frac{1}{2}$

Then, in order to find the range, let's calculate the inverse function of $y = \frac{5 x + 3}{1 - 2 x}$:

You need some steps:

$y \left(1 - 2 x\right) = 5 x + 3$

$y - 2 x y = 5 x + 3$

$5 x + 2 x y = y - 3$

$x \left(5 + 2 y\right) = y - 3$

$x = \frac{y - 3}{5 + 2 y}$

so the range is obtained by the values y:

$5 + 2 y \ne 0$

or

$y \ne - \frac{5}{2}$