# What is the domain and range of y=1/(3x-2)?

Apr 8, 2017

$x \in \mathbb{R} , x \ne \frac{2}{3}$
$y \in \mathbb{R} , y \ne 0$

#### Explanation:

The denominator of y cannot be zero as this would make y $\textcolor{b l u e}{\text{undefined}} .$Equating the denominator to zero and solving gives the value that x cannot be.

$\text{solve "3x-2=0rArrx=2/3larrcolor(red)" excluded value}$

$\Rightarrow \text{domain is } x \in \mathbb{R} , x \ne \frac{2}{3}$

$\text{Rearrange to make x the subject}$

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

$\Rightarrow 3 x y - 2 y = 1$

$\Rightarrow 3 x y = 1 + 2 y$

$\Rightarrow x = \frac{1 + 2 y}{3 y}$

$\text{solve " 3y=0rArry=0larrcolor(red)" excluded value}$

$\Rightarrow \text{range is } y \in \mathbb{R} , y \ne 0$
graph{1/(3x-2) [-10, 10, -5, 5]}