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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.

Guest Jul 10, 2018
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$$q(x) = \frac{\sqrt{x}}{\sqrt{1-x^2}}$$

Note that.....for the function in the numerator, the domain  is     [ 0, ∞ )

For the function inthe denominator, the domain is (-1, 1)

But....we must use the most restrictive domain possible.....this is  [ 0, 1 )

Here is a graph that will confirm  this  :

https://www.desmos.com/calculator/ywedl27com

CPhill  Jul 10, 2018