Bijective function

Let $f\colon A\to B$ be a function . Then $f$ is bijective if it is both injective and surjective .

Equivalently, $f$ is bijective if and only if it has an inverse function .

Examples:

• $f\colon\mathbb{Z}\to\mathbb{Z}$ given by $f(n)=n+1$ is bijective.
• The map $g\colon\mathbb{R}\to(0,\infty)$ given by $g(x)=e^x$ is bijective.
• The map $h\colon\mathbb{R}\to\mathbb{R}$, $h(x)=x^2$, is not bijective.