Question

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

Answer 1

`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]`.