Show that the function f: R → R : f(x) = x 5 is one - one and onto.

Question

Philoid · Accepted Answer

To show: f: R → R : : f(x) = x⁵ is one - one and onto.

Proof:

f(x) = x⁵

⇒y = x⁵

Since the lines do not cut the curve in 2 equal valued points of y, therefore, the function f(x) is one - one.

The range of f(x) = ( - ∞,∞) = R(Codomain)

∴f(x) is onto

Hence, showed f: R → R : f(x) = x⁵ is one - one and onto.