Q. 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]
Explanation
(c)
Given, $f(x) = \frac{1}{\sqrt{4 - x^{2}}}$
For domain of $f(x)$,
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 4 - x^{2} > 0$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x^{2} < 4$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ - 2 < x < 2$
$\therefore$ Domain$= ( - 2,\ 2)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.