How do you find the domain of square root of 1-x^2?

1 Answer
alex · Stefan V.
Jun 21, 2018

#sqrt(1-x^2)# has the domain #[-1,1]#.

Explanation:

A square root with a negative number under the root cannot produce a real number. This means that #1-x^2# must be greater than or equal to zero.

Squaring a real number will always produce a positive number, so #x^2# must be equal to or smaller than #1#. This means #x# is between #0# and #1#, giving the domain of #[0,1]#.

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