Question

Find the domain of definition of the following function:
$y=\sqrt{(x^2-3x-10)}\log (x-3)$

Answer 1

$x^2-3x-10\ge 0(x-5)(x+2)\ge 0x\in (-\infty ,-2]\cup [5,\infty )$

For

$\log (x-3)\ge 0x-3>0x>3$

Taking intersection, we get

$x\in [5,\infty )$