Question

Find the domain of definition of the following function:
$y=\sqrt{\log \frac{1-2x}{x+3}}$

Answer 1

$y=\sqrt{\log \frac{1-2x}{x+3}}$

$⟹\frac{1-2x}{x+3}>0⟹x\in (-3,\frac{1}{2})$

And $\log \frac{1-2x}{x+3}\ge 0⟹\frac{1-2x}{x+3}-1\ge 0⟹\frac{-3x-2}{x+3}\ge 0⟹x\in [-3,-\frac{2}{3}]$

So $x\in (-3,-\frac{2}{3})$