What is Function?

We write $y = f(x)$. A graph shows a function if no vertical line meets it at more than one point. For $f(x) = \sqrt{x}$ the domain is $x \geq 0$, because the square root of a negative number is not real. For $f(x) = \dfrac{1}{x}$ the domain is all real numbers except $0$. The inverse function undoes the first one. It exists when each output comes from only one input.