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

Related questions
See all questions in Domain and Range of a Function
Impact of this question
1680 views around the world
You can reuse this answer
Creative Commons License