Question

Find the domain of definition of the following function:
$y=\sqrt{\log \frac{3-x}{x}}$

Answer 1

$\log \left(\frac{3-x}{x}\right)\ge 0\Rightarrow \frac{3-x}{x}\ge 1andx>0\Rightarrow 3-x\ge x\frac{3}{2}\ge x,x>0$

Hence,$x\in (0,\frac{3}{2}]$