If there is a variable "$x$" , and another is "$y$", and let's say I know the relation between them as
Now, I want to use them in the explanation of some mathematical theory/proof/equation etc. Why a different notation called $f(x)$ ( function of $x$ ) is used to represent $y$ ? Why can't y itself be used ? Cannot i just remember that "$y$" has some relation with "$x$" . Is their some other importance also, other than representing a relation of "$y$" with "$x$", when some term like $f(x)$ is used ?