Question

Find the domain of definition of the following function.
$y={\log }_2\frac{x-2}{x+2}.$

Answer 1

$y={\log }_2\left(\frac{x-2}{x+2}\right)$

$(x+2)(x-2)>0$

$x>-2$

$x>2$ and

$x<-2$

$x<2$

So, the domain of $y=(-\infty ,-2)\bigcup (2,\infty )$