Main Question or Discussion Point
I have a question regarding notational conventions. From previous research, I have determined that, for the general function ƒ(x), x is the input, ƒ is the relation or "law of correspondence," and ƒ(x) is the output, the result of applying the rule ƒ to the variable x. However, almost ubiquitously in other texts and websites, they refer to the entire function as ƒ(x), e.g., "let's examine the function ƒ(x) = x2 + 1." My question, then, is what is right? Why do some authors say that ƒ is the function, while others say that ƒ(x) is the function? This distinction might seem rather pedantic, but I am nonetheless still bothered by it.