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KCET2009MathematicsFunctions

On the set of integers Z , define f: Z Z as f(n)= array ll n 2 , & n is even 0, & n is odd array . then f is

Options

  1. Ainjective but not surjective
  2. Bneither injective nor surjective
  3. Csurjective but not injective
  4. Dbijective

Correct answer

C. surjective but not injective

Step-by-step solution

Given, f(n)= cases n 2 , & n is even 0, & n is odd cases Here, we see that for every odd values of z , it will give zero. It means that it is a many one function. For every even values of z , we will get a set of integers (- , ) . So, it is onto. Hence, it is surjective but not injective.

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