Answer
Domain: $(-\infty,1)\cup(1,+\infty)$
Work Step by Step
For a logarithmic function to be defined,
its argument must be POSITIVE,
So, g is defined for
$x^{2}-1>0$
$x^{2}>1$
The square of a real number x is greater than 1 if $|x|>1$
(all numbers less than -1 or greater than 1)
$x1$
In interval notation,
$x\in(-\infty,1)\cup(1,+\infty)$
Domain: $(-\infty,1)\cup(1,+\infty)$
