Question

Find the domain of definition of the following function.
$f\left(x\right)=\log \frac{x+3}{x+1}.$

Answer 1

$f\left(x\right)=\log \frac{x+3}{x-1}$

$(x+3)(x+1)>0$

$x>-3$

$x>-1$ and

$x<-3$

$x<-1$

So,the domain of $y=(-\infty ,-3)\bigcup (-1,\infty )$