Find domain of the function $$f(x) = sqrt(x) + 2/x + sqrt(-x).$$ Express your answer in interval notation.

Answer 1

The expression $\sqrt{x}$ is defined only for $x \geq 0$, the expression $\frac{2}{x}$ is defined for $x \neq 0$, and the expression $\sqrt{-x}$ is defined only for $-x \geq 0$, or $x \leq 0$. Therefore, the domain of $f(x)$ is the intersection of these interval: $x \in \boxed{(-\infty, 0] \cup (0, \infty)}$.