Surjective function

Surjectivity can be expressed using the image: $f$ is surjective exactly when $f(A)$ equals its codomain $B$. Surjectivity is one of the two conditions (along with injectivity) needed for a bijection.

• The function $f:\mathbb{R}\to\mathbb{R}$ given by $f(x)=x^3$ is surjective, since every real number has a real cube root.
• The parity map $p:\mathbb{Z}\to\{0,1\}$ (even $\mapsto 0$, odd $\mapsto 1$) is surjective.