Question

If $f:Z\to Z$ is defined by $f\left(x\right)=\{\begin{array}{cc}\frac{x}{2}& ifxiseven\\ 0& ifxisodd\end{array}$ then f is

• A. Onto but not one to one
• B. One to one but not onto
• C. One to one and onto
• D. Neither one to one nor onto

Answer 1

The correct option is A Onto but not one to one

f is onto and but not one to one as all odd values x has a 0 assigned in $f\left(x\right).$

Function is onto as every element in $f\left(x\right)$ is mapped to some element in $x.$