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

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Answer 1 · 2016-12-08T12:10:18

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

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

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

Hence: $f (x)$ $f(x)$ is defined for $| x | > 2$ $absx> 2$

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

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

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

How do you find the domain of ln(x^2-4)ln(x2−4)ln(x^2-4)?