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
onto but not one-one
one-one but not onto
one-one and onto
neither one-one nor onto
Solution
Clearly, it is onto but not one-one. Since each odd integer mapped with zero.