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Question

The mapping f:ℕ→ℕ is given by f(n)=1+n2, n belongs to ℕ, where ℕ is the set of natural numbers, is :


A

one-one and onto

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B

onto but not one-one

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C

one-one but not onto

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D

neither one-one nor onto

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Solution

The correct option is C

one-one but not onto


Explanation for the correct option

Given function, f(n)=1+n2

If n=1, value of f(n)=2

If n=2, value of f(n)=5

If n=3, value of f(n)=10

Thus,f(n) is one-one.

Bur clearly, range ≠ co-domain,, range⊂co-domain

So, f(n) is not onto.

Hence, Option(C) is the correct answer.


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