Question

The domain of the real function $f(x)=\frac{1}{\sqrt{4-x^2}}$ is

• A. the set of all real numbers
• B. the set of all positive real numbers
• C. $(-2,2)$
• D. $[-2,2]$

Answer 1

Answer: (C)

$f(x)$ assumes real values, if
$4-x^2>0$
$\Rightarrow x^2-4<0$
$\Rightarrow (x+2)(x-2)<0$
$\Rightarrow x\in (-2,2)$
$\therefore$ Domain of $f=(-2,2)$