# Inverse (in Algebra) Given a [[Function (in Algebra)|function]] $f$, that function's inverse $f^{-1}$ is said to exist if for each member of the $f$ domain ($x$) the following holds. $f^{-1}(f(x)) = x$ In other words, the function $f$ is a 1-to-1 function i.e. $f$ maps each member of the $f$ domain to exactly one member of the $f$ codomain in such a way that each member of the codomain is mapped by only one domain member. Graphically, a function has an inverse if it is symmetric about the $x=y$ line.