# How do you find the domain of f(x) = (x+7)/(x^2-4)?

May 8, 2018

$\left(- \infty , - 2\right) \cup \left(- 2 , 2\right) \cup \left(2 , \infty\right)$

#### 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.

$\text{solve } {x}^{2} - 4 = 0 \Rightarrow {x}^{2} = 4$

$\Rightarrow x = - 2 , x = 2 \leftarrow \textcolor{red}{\text{excluded values}}$

$\Rightarrow \text{domain } \left(- \infty , - 2\right) \cup \left(- 2 , 2\right) \cup \left(2 , \infty\right)$
graph{(x+7)/(x^2-4) [-10, 10, -5, 5]}