What does the expression (f/g)(x) represent?

The expression ((f/g)(x)) represents the function formed by dividing (f(x)) by (g(x)). Specifically, when you see the notation ((f/g)(x)), it denotes the application of the division operation between the two functions (f) and (g) evaluated at the input (x).

This means that for any value of (x) in the domain where (g(x) \neq 0), you would take the output of (f(x)) and divide it by the output of (g(x)). This is a standard way of expressing the relationship between two functions where one function modifies the output of another through division. Understanding this notation is crucial in exploring function behaviors, including finding limits, analyzing ratios, and studying asymptotic properties of functions.