The notation f(x) = (3 x) refers to the binomial coefficient, commonly expressed as "3 choose x," which represents the number of ways to choose x items from a set of 3. This coefficient serves as a crucial part of the probability distribution function for a binomial distribution. However, the discussion highlights that using this notation alone does not yield a valid probability distribution since it does not sum to 1. It suggests that the function f(x) likely requires a multiplier, typically involving a probability term, to form a complete distribution. The correct interpretation involves the binomial distribution formula f(x) = (3 choose x) p^x (1 - p)^(3 - x) for x = 0, 1, 2, or 3.