# How do you find the domain and range for y = (3(x-2))/x?

Jun 29, 2018

Domain : $x < 0 \text{ or} x > 0$

Range : -6 / (x - 3)#

#### Explanation:

The domain is the set of all possible x-values which will make the function "work", and will output real y-values.

Find the domain and range of the function y = 1 x + 3 − 5 . To find the excluded value in the domain of the function, equate the denominator to zero and solve for .

The range of the function is same as the domain of the inverse function.

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

Domain : When x = 0, point x=0 is undefined.

The function domain $x < 0 \text{ or } x > 0$

Range : Set of values of the dependent variable for which a function is defined.

Function range is the combined domain of the inverse functions.

$\text{inverse of } \frac{3 \left(x - 2\right)}{x} : - \frac{6}{x - 3}$

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

Jun 29, 2018

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

#### Explanation:

The denominator of y cannot be zero as this would make y undefined. Equating the denominator to zero and solving gives the value that x cannot be.

$x = 0 \leftarrow \textcolor{red}{\text{excluded value}}$

$\text{domain is } x \in \mathbb{R} , x \ne 0$

$\left(- \infty , 0\right) \cup \left(0 , \infty\right) \leftarrow \textcolor{b l u e}{\text{in interval notation}}$

$\text{to find the range, rearrange making x the subject}$

$x y = 3 x - 6$

$x y = 3 x = - 6$

$x \left(y - 3\right) = - 6$

$x = - \frac{6}{y - 3}$

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

$\text{range is } y \in \mathbb{R} , y \ne 3$

$\left(- \infty , 3\right) \cup \left(3 , \infty\right)$
graph{(3x-6)/x [-20, 20, -10, 10]}