A function f from the set of natural numbers to integers defined by f(n)= array l n-1 2 , when n is odd - n 2 , when n is even array . is

Step-by-step solution

The function f: N Z is defined as f(n) = n-1 2 if n is odd and f(n) = - n 2 if n is even. To check for one-one, consider two distinct natural numbers n₁ and n₂ . If n₁ is odd and n₂ is even, f(n₁) = n₁-1 2 0 and f(n₂) = - n₂ 2 To check for onto, consider any integer k Z . If k 0 , we can choose n = 2k+1 , which is an odd natural number, such that f(2k+1) = 2k+1-1 2 = k . If k Therefore, the function is both one-one and onto. Answer: one-one and onto