What is the domain of $\sqrt{4 - x^{2}}$ $sqrt(4-x^2)$ ?

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Answer 1 · 2018-04-19T11:58:19

$[- 2, 2]$ $color(blue)([-2,2]$

If:

$\sqrt{4 - x^{2}}$ $sqrt(4-x^2)$ is defined only for real numbers then:

$4 - x^{2} \geq 0$ $4-x^2>= 0$

$x^{2} \leq 4$ $x^2<= 4$

$x \leq 2$ $x<=2$

$x \geq - 2$ $x>=-2$

$:.$

$[-2,2]$

Answer 2 · 2018-04-19T12:03:40

$-2 <= x <= 2$

The square roots are only defined when the expression under the square root is non-negative.

$4 - x^2 >=0$
$|x| <= 2$
$-2 <= x <= 2$

What is the domain of sqrt(4-x^2)√4−x2sqrt(4-x^2)?