### Let X be a non-empty set and f a mapping of X into itself. Show that f is one-to-one onto iff there exists a mapping g of X into itself such that fg = gf = iX. If there exists a mapping g with this property, then there is only one such mapping. Why?

Topology Sets and Functions (XXXIX) Functions Let X be a non-empty set and f a mapping of X into itself. Show that f is one-to-one onto iff there exists a mapp