Question

Find the domain of definition of the following function:
$y=\sqrt{4x-x^2}-{\log }_3(x-2)$

Answer 1

For

$\sqrt{4x-x^2}4x-x^2\ge 0x^2-4x\le 0x(x-4)\le 0x\in [0,4]$

For

${\log }_3(x-2)x-2>0x>2$

Taking intersection,

$x\in (2,4]$