Answer :

(i) f : N N : f(x) = x2 is one - one into.


f(x) = x2


y = x2



Since the function f(x) is monotonically increasing from the domain N N


f(x) is one one


Range of f(x) = (0,∞)≠N(codomain)


f(x) is into


f : N N : f(x) = x2 is one - one into.


(ii) f : Z Z : f(x) = x2 is many - one into


f(x) = x2


y = x2


in this range the lines cut the curve in 2 equal valued points of y, therefore, the function f(x) = x2 is many - one .


Range of f(x) = (0,∞)≠Z(codomain)


f(x) is into



f : Z Z : f(x) = x2 is many - one into


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