Let $Z$ denote the set of integers define $f: Z \rightarrow Z$ by $f(x)=\left\{\begin{array}{ll}\frac{x}{2},…

Let $Z$ denote the set of integers define $f: Z \rightarrow Z$ by $f(x)=\left\{\begin{array}{ll}\frac{x}{2}, & x \text { is even } \\ 0, & x \text { is odd }\end{array}\right.$ then $f$ is
  1. onto but not one-one
  2. one-one but not onto
  3. one-one and onto
  4. neither one-one nor onto

Solution

Clearly, it is onto but not one-one. Since each odd integer mapped with zero.

Asked in: AP EAMCET 2001

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