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Find the domain of the function $$f(x) = \frac{\sqrt{x}}{\sqrt{x^2}}.$$ Express your answer as an interval or as a union of intervals.

 Feb 19, 2024
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For the function f(x), you can have x be any real number other than negative numbers because the square root of a negative number is imaginary. We can see in the denominator that x can be negatives because it gets squared which makes it positive, but that doesn't change the domain because the top would still be imaginary. That means the smallest possible x value to be inputted into the function is 0.

 

This makes the domain [0, inf).

 Feb 20, 2024

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