How do you find the domain of #sqrt(4 - x²)#?

1 Answer
Alan P.
May 8, 2016

#x in [-2,+2]#

Explanation:

The domain is the set of values for which the expression is valid.

In the given example:
#color(white)("XXX")sqrt(4-x^2)#
we know that the argument of the square root must be greater than or equal to zero (assuming Real values; the square root of a negative value does not exist as a Real value).

Therefore
#color(white)("XXX")4-x^2 >=0#

#color(white)("XXX")rarr x^2 <= 4#

#color(white)("XXX")rarr -2 <= x <= +2#

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