If x is a point in the set X, and A is a subset of X, and f is a function that maps X to the set Y, f(x) is a point in Y and f(A) is a subset of Y. If y is a point in Y and B is a subset of Y, f???1(y) is only a function if f is one-to-one and onto, but f???1(B) is always a function.