# How do you find the domain of ln(x^2-4)?

Dec 8, 2016

The domain of $f \left(x\right)$ is $\left(- \infty , - 2\right) \cup \left(+ 2 , + \infty\right)$

#### Explanation:

$f \left(x\right) = \ln \left({x}^{2} - 4\right)$

Since $\ln x$ is defined for $x > 0$
$f \left(x\right)$ is defined for ${x}^{2} - 4 > 0$

Hence: $f \left(x\right)$ is defined for $\left\mid x \right\mid > 2$

The domain of a function is the set of input values $\left(x\right)$ for which the function $f \left(x\right)$ is defined.

Therefore the domain of $f \left(x\right)$ in this example is: $\left(- \infty , - 2\right) \cup \left(+ 2 , + \infty\right)$

This can be seen by the graph of $f \left(x\right)$ below.
graph{ln(x^2-4) [-10, 10, -5, 5]}