Question

Find the domain of the following function :

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

• A. $[-1,1]$
• B. $(-\infty ,\infty )$
• C. $[-2,2]$
• D. None of these

Answer 1

Answer: (C)

$[-2,2]$

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

Clearly, $f\left(x\right)$ assumes real values for all x satisfying

$\Rightarrow 4-x^2\ge 0$

$\Rightarrow -(x^2-4)\ge 0$

$\Rightarrow x^2-4\le 0$

$\Rightarrow (x-2)(x+2)\le 0$

$\therefore x\in [-2,2]$

Hence, Domain (f) = $[-2,2]$