### 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 defined and meaningful.
I see that the function has a square root in the denominator, which means that I need to avoid two possible sources of trouble: negative values and zero values.
If x is negative, then the square root of x is not a real number, and the function is undefined.
If x is zero, then the function is undefined because I cannot divide by zero.
So, the domain of the function is the set of all positive real numbers, or x > 0.
To express this in interval notation, I use a parenthesis to indicate that x cannot be equal to zero, and an infinity symbol to indicate that there is no upper bound on x. The interval notation is: (0, ∞).