The function `f:NtoN,N` being the set of of natural numbers, defined by f(x)=2x+3 is

Explanation

(i) To test whether f is one-one (injective):
Let `x_(1), x_(2) in` domain N.
Let `f(x_(1)) = f (x_(2)) rArr 2x_(1) + 3 = 2x_(2) + 3 rArr x_(1) = x_(2)`. Hence f is injective.
(ii) To rest whether f is onto (surjective) :
Let `y in` co-domain `N rArr y` is a natural number. brgt Let `y = f(x) rArr y = 2x + 3 rArr x = (y - 3)/(2) cancelin` domain N, when y = 2.
Thus `2 in` co-domain N is not the image of any `x in` domain N and hence f is not onto (surjective).