Recall that a function f must pass the vertical line test to guarantee that each input gives at most one output.

Since f−1 is also a function, it too must pass the vertical line test. But since the graph of f−1(x) is a reflection of the graph of f(x) in the line y=x, the graph of f(x) must then pass the horizontal line test:

A function that passes the horizontal line test is said to be one to one - each input yields exactly one distinct output. Such a function is said to be invertible, which means f−1 exists.