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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)

Options

  1. Aone-one and onto
  2. Bone-one and into
  3. Cmany-one and onto
  4. Dmany-one and into

Correct answer

A. one-one and onto

Step-by-step solution

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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