Show that the function f: R → R : f(x) = 1 + x 2 is many - one into.

Question

Philoid · Accepted Answer

To show: f: R → R : f(x) = 1 + x² is many - one into.

Proof:

f(x) = 1 + x²

⇒y = 1 + x²

Since the lines cut the curve in 2 equal valued points of y therefore the function f(x) is many one.

The range of f(x) = [1,∞)≠R(Codomain)

∴f(x) is not onto

⇒f(x) is into

Hence, showed that f: R → R : f(x) = 1 + x² is many - one into.