Show that the function f : R → R : f(x) = x 4 is many - one and into.

Question

Philoid · Accepted Answer

To show: f: R → R : f(x) = x⁴ is many - one into.

Proof:

f(x) = x⁴

⇒y = x⁴

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

The range of f(x) = [0,∞)≠R(Codomain)

∴f(x) is not onto

⇒f(x) is into

Hence, showed that f: R → R : f(x) = x⁴ is many - one into.