Question

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

Answer 1

For

$\log (1-\sqrt{4-x^2})1-\sqrt{4-x^2}>01>\sqrt{4-x^2}1>4-x^2{x}^2-3>0(x+\sqrt{3})(x-\sqrt{3})>0x\in (-\infty ,-\sqrt{3})\cup (\sqrt{3},\infty )$

Also,

$4-x^2\ge 0x^2-4\le 0x\in [-2,2]$

Taking intersection, we get

$x\in [-2,-\sqrt{3})\cup (\sqrt{3},2]$