If f : N → Z defined as f n = n - 1 2 : if n is o d d - n 2 : if n is e v e n and g : N → N defined as g n = n - - 1 n , then f o g is (where, N is the set of natural numbers and Z is the set of integers)

Question

If f : N → Z defined as f n = n - 1 2 : if n is o d d - n 2 : if n is e v e n and g : N → N defined as g n = n - - 1 n , then f o g is (where, N is the set of natural numbers and Z is the set of integers), one-one and onto, one-one and into, many-one and onto, many-one and into

MARKS App · Accepted Answer

f o g : N → Z f g 1 = f 2 = - 1 , f g 3 = f 4 = - 2 f g 2 = f 1 = 0 , f g 4 = f 3 = 1 Clearly, f g n = - 1 n = 1 - 2 n = 3 - 3 n = 5 : : : : and f g n = 0 n = 2 1 n = 4 2 n = 6 : : ∴ f o g is one-one & onto

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