What is the domain of #sqrt(4-x^2)#?

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Answer 1 · 2018-04-19T11:58:19

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

If:

#sqrt(4-x^2)# is defined only for real numbers then:

#4-x^2>= 0#

#x^2<= 4#

#x<=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#