Q7 of 99 Page 34

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.


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