# How do you find the domain of f(x) = (x+9)/(x^2-361)?

May 31, 2018

The domain is $x \in \left(- \infty , - 19\right) \cup \left(- 19 , 19\right) \cup \left(19 , + \infty\right)$

#### Explanation:

The denominator must be $\ne 0$

Therefore,

${x}^{2} - 361 \ne 0$

${x}^{2} \ne 361$

$x \ne \sqrt{361}$

$x \ne 19$ and $x \ne - 19$

The domain is $x \in \left(- \infty , - 19\right) \cup \left(- 19 , 19\right) \cup \left(19 , + \infty\right)$

graph{(x+9)/(x^2-361) [-36.53, 36.52, -18.28, 18.27]}

May 31, 2018

$x \in \mathbb{R} , x \ne \pm 19$

#### Explanation:

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

$\text{solve "x^2-361=0rArrx=+-19larrcolor(red)"excluded values}$

$\text{domain } x \in \mathbb{R} , x \ne \pm 19$

$\text{this can be expressed in "color(blue)"interval notation}$

$x \in \left(- \infty , - 19\right) \cup \left(- 19 , 19\right) \cup \left(19 , \infty\right)$
graph{(x+9)/(x^2-361) [-40, 40, -20, 20]}