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# What is the domain of the real-valued function: ​Express your answer as an interval or as a union of intervals.

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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.

Mar 8, 2019

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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

Mar 8, 2019