Question

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

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

Answer 1

The correct option is C $(-2,2)$

Given,

$f\left(x\right)=\frac{1}{\sqrt{4-x^2}}$

$f\left(x\right)$ is real if $4-x^2>0$

Since, it is given that the function $f\left(x\right)$ is real
$\Rightarrow 4-x^2>0$
$\Rightarrow x^2<4$
$\Rightarrow -2<x<2$

$\therefore$ Domain of $f\left(x\right)$ is $(-2,2)$