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.

Answer 1

For this function to be defined, both the numerator and denominator must be defined. The numerator is defined for all nonnegative values of $x$, and the denominator is defined for all nonzero values of $x$. Therefore, the domain of the function is the set of all nonnegative real numbers excluding zero, or $\boxed{(0,\infty)}$.