A function f from a set X to Y is called onto, if for every y ∈ Y there exist x ∈ X such…

A function f from a set X to Y is called onto, if for every
y ∈ Y there exist x ∈ X such that f (x) = y. Unless the contrary is specified, a real function is onto if it takes all real values, otherwise it is called into function. Thus, if X and Y are finite sets, then f cannot be onto If Y contains more element than X.
The polynomial function
P (x) = a₀xⁿ + a₁x^n–1 + a₁x^n–2 + .... + a_n ,
where a₀ ≠ 0, is onto, for