# How do you find the domain of g(x)=6/(9-5x)?

Aug 3, 2018

$x \in \mathbb{R} , x \ne \frac{9}{5}$

#### Explanation:

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

$\text{solve "9-5x=0rArrx=9/5larrcolor(red)"excluded value}$

$\text{domain is } x \in \mathbb{R} , x \ne \frac{9}{5}$

$\left(- \infty , \frac{9}{5}\right) \cup \left(\frac{9}{5} , \infty\right) \leftarrow \textcolor{b l u e}{\text{in interval notation}}$
graph{6/(9-5x) [-10, 10, -5, 5]}

Aug 3, 2018

$x \in \mathbb{R} , x \ne \frac{9}{5}$

#### Explanation:

The only thing that will make $g \left(x\right)$ undefined is when the denominator is zero, so let's set it to zero to find any excluded values in the domain.

$- 5 x + 9 = 0 \implies - 5 x = - 9 \implies x = \frac{9}{5}$

The value $x = \frac{9}{5}$ is not included in our domain, so we can say

$x \in \mathbb{R} , x \ne \frac{9}{5}$

We can even see this graphically, as we have a vertical asymptote at $x = \frac{9}{5}$.

graph{6/(9-5x) [-10, 10, -5, 5]}

Hope this helps!