Answer :

Let f : N N, be a function given by f(x) = 2x.


In order to prove that f is one-one, it is sufficient to prove that f(x1)=f(x2) x1=x2 x1, x2 N


Now, let f(x1) = f(x2)


2x1= 2x2


x1= x2


f is one-one.


f is not onto, as for 1 N, there does not exist any x in N such that f(x) = 2x = 1.


Thus, f : N N, be a function given by f(x) = 2x, which is one-one but not onto.


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