I have two functions that I want to compare - call them f(x) and g(x), x is real, and f and g are R -> R. What is the most appropriate way to compare these functions? I should note that both of these functions are Riemann integrable - they are bounded and continuous.

One comparison could be h(x) = f(x)-g(x). Taking this a step further, we could integrate h to produce a numerical value for the difference between these two functions.

Another comparison is h(x) = f(x)/g(x). This function won't be continuous or bounded at the roots of g. We could also do log(h(x)).

Are there other ways to compare functions?