how to prove that a given function is onto?
Recall the definition,
A function f: X → Y is said to be onto (or surjective) if every element of Y is the image of some element of x in X under f. In other words, f is onto if " for y ∈ Y, there exist x ∈ X such that f (x) = y.
I.e., f: X → Y is onto if and only if the range of f = Y.
So, in order to show that f is onto; take any element (say y) of Y and than, check whether there exists x ∈ X such that f (x) = y.
Hope! You got the required procedure.