Surjective function
Discussion: The cubic equation x3-3x-yo=0 has real coefficients (a3=1, a2=0, a1=–3, a0=–yo). Every such cubic equation has at least one real root. Since the domain of the polynomial is ℝ, the means that ther is at least one pre-image xo in the domain. That is, (x0)3-3x0-yo=0. So the function is a surjection. (However, this function is not an injection. For example, yo=2 has 2 pre-images: x=–1 and x=2. In fact, every y, –2≤y≤2 has at least 2 pre-images.)