Question

Find the domain of the real valued logarithmic function $f$ given below
$f\left(x\right)=\ln (x^2-9)$

Answer 1

$f\left(x\right)=\ln (x^2-9)$
Thus, $f\left(x\right)$ is real valued if $(x^2-9)>0$
$⟹x^2>9$ and $\left|x\right|>3$
$⟹x<-3$ or $x>3$

So, domain of given function is given by $(-\infty ,-3)\cup (3,\infty )$.