f(x) = x²

⇒y = x²

in this range the lines cut the curve in 2 equal valued points of y, therefore, the function f(x) = x² is many - one .

Range of f(x) = (0,∞)≠R(codomain)

∴f(x) is into

∴ f : R → R: f(x) = x² is many - one into