Let f: N → N be defined by

State whether the function f is bijective. Justify your answer.

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Solution

f: N → N is defined as

It can be observed that:

∴ f is not one-one.

Consider a natural number (n) in co-domain N.

Case I: n is odd

∴n = 2r + 1 for some r ∈ N. Then, there exists 4r + 1∈N such that

.

Case II: n is even

∴n = 2r for some r ∈ N. Then,there exists 4r ∈N such that.

∴ f is onto.

Hence, f is not a bijective function.

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