### Instruction: Find the domain of the function
\[h(x) = \frac{3x - 1}{\sqrt{x - 5}}.\].### Response: To find the domain of a function, I need to identify the values of x that make the function well-defined and real-valued.
For this function, there are two possible sources of trouble: division by zero and square root of a negative number.
To avoid division by zero, I need to make sure that the denominator is not zero.
That means I have to exclude the value of x that makes x - 5 equal to zero, which is x = 5.
To avoid square root of a negative number, I need to make sure that the radicand is not negative.
That means I have to exclude the values of x that make x - 5 less than zero, which are all the values of x that are smaller than 5.
Putting these two conditions together, I see that the domain of h(x) is the set of all x that are greater than 5, or in interval notation, (5, infinity).