Question

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

Answer 1

For

$\log \left(\frac{x}{x-2}\right)\frac{x}{x-2}>0x(x-2)>0,x\ne 2x\in (-\infty ,0)\cup (2,\infty )$

and

$\sqrt{x-3}x-3\ge 0x\ge 3$

Taking intersection, we get

$x\in [3,\infty )$