How to tell if $f(n) = 2 \left\lfloor\frac n2\right\rfloor$ from $\mathbb{Z}$ to $\mathbb{Z}$ is onto?

Question

How can we tell if the function $f(n) = 2 \left\lfloor\frac n2\right\rfloor$ from $\mathbb{Z}$ to $\mathbb{Z}$ is onto? Thanks!

Answer 1

A function $f:A\to B$ is onto if for every $b\in B$ there is some $a\in A$ such that $f(a)=b$. Here the function is not onto because there is no value that is mapped to $1$. Applying $f$ always yields an even integer.