# How do you find the range of f(x)= 2/(3x-1)?

Mar 21, 2018

The range is $\mathbb{R} - \left\{0\right\}$

#### Explanation:

The function is

$f \left(x\right) = \frac{2}{3 x - 1}$

To find the range, proceed as follows

Let $y = \frac{2}{3 x - 1}$

Therefore,

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

$y 3 x - y = 2$

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

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

Therefore,

As the denominator is $\ne 0$

$y \ne 0$

The range is $\mathbb{R} - \left\{0\right\}$

graph{2/(3x-1) [-10, 10, -5, 5]}