Horizontal line test

Horizontal line test. If a function $f$ is one-to-one, every ``horizontal line'' should intersect the graph of $f$ in at most one point.

Alternative definition of inverse function. Suppose that $f$ is a one-to-one function with domain $ D$ and range $ R$. Then the inverse function $ f^{-1}$ can be viewed as the set $ W = \{(x, f^{-1}(x)): x \in R\}$ on the rectangular coordinate system. Furthermore, the set $ W$ is given by

$\displaystyle W = \{(x, f^{-1}(x)): x \in R\}
= \{(f(x), x): x \in D\}.

Department of Mathematics
Last modified: 2005-09-29