Question

Find the domain of definition of the following function:
$y=\sqrt{{\log }_{0.3}\frac{x-1}{x+5}}$

Answer 1

${\log }_{0.3}\frac{x-1}{x+5}\ge 0$ also $x>-5$

As the base is less than $1$

$0<\frac{x-1}{x+5}\le 1$

Solving inequalities

$x>1$

Taking intersection we get $x\in (1,\infty )$