The essential idea
in a function from one set, X, to another set, Y, is that
for every element, x, in X
there is associated in some way
one and only one element of Y,
which is denoted by f(x).
We refer to the function in symbols as follows:
The x in the expression f(x) is often called the argument of the function.
The argument is whatever appears inside of the parenthesis.
f(x) is the value of the function at x.
A formal definition is the following:
A function from X to Y,
is any subset of the cartesian product of X and Y which has the property that
each element of X appears in one and only one of the ordered pairs in .
Thus, for each element of X there is associated one and only one element of Y.
A More General Definition of the word Function :