Question

Find the domain of definition of the following function:
$f\left(x\right)y=\sqrt{4x-x^3}+\log (x^2-1).$

Answer 1

For

$\sqrt{4x-x^3}4x-x^3\ge 0x^3-4x\le 0x(x^2+2)(x-2)\le 0x\in (-\infty ,-2]\cup [0,2]$

and

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

Taking intersection, we get

$x\in (-\infty ,-2]\cup (1,2]$