Show that the function f: R → R : f(x) = x5 is one - one and onto.
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.