### Instruction: What is the domain of the function $$u(x) = \frac{1}{\sqrt x}~?$$ Express your answer in interval notation.### Response: To find the domain of a function, I need to identify the values of x that make the function undefined or invalid.
In this case, the function involves a square root and a fraction, so I need to avoid negative values and zero in the radicand and the denominator.
That means I need x to be strictly positive, or x > 0.
In interval notation, this is written as (0, +\infty), where the parentheses indicate that the endpoints are not included in the domain.
So the domain of u(x) is (0, +\infty).