Question

Find the domain of definition of the following function:
$y=\sqrt{4x-x^2}+\log (x^2-1)$

Answer 1

For

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

For

$\log (x^2-1)x^2-1>0(x+1)(x-1)>0x\in (-\infty ,-1)\cup (1,\infty )$

Taking intersection, we get

$x\in (1,4]$