What is the domain of the real-valued function: \(q(x) = \frac{\sqrt{x}}{\sqrt{1-x^2}}\)Express your answer as an interval or as a union of intervals.
We have a couple of things to consider
First.....the domain of the function ih the numerator is x ≥ 0
For the function in the denominator.....1 - x^2 must be greater than 0
So
1 - x^2 > 0
( 1 - x) ( 1 + x ) > 0
If -1 < x < 1 this is true
But....the restriction in the denominator makes the true domain 0 ≤ x < 1