Question

Find the domain of definition of the following function.
$y,=\sqrt{\frac{x+3}{5-x}}.$

Answer 1

$y=\sqrt{\frac{x+3}{5-x}}$

$x+3\ge 0$

$5-x>0$

$x+3\ge 0$

$x\ge -3$

$5-x>0$

$x<5$

So, $-3\le x<5$

The Domain of $y=[-3,5)$