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
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