Q12 of 99 Page 34

Prove that the function f : N → N : f(n) = (n2 + n + 1) is one - one but not onto.

In the given range of N f(x) is monotonically increasing.


∴f(n) = n2 + n + 1 is one one.



But Range of f(n) = [0.75,∞)≠N(codomain)


Hence,f(n) is not onto.


Hence, proved that the function f : N → N : f(n) = (n2 + n + 1) is one - one but not onto.


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