mathematics Given a function, f : D -@# C, a function g : C

-@# D is called a left inverse for f if for all d in D, g (f d)

= d and a right inverse if, for all c in C, f (g c) = c and an

inverse if both conditions hold. Only an injection has a

left inverse, only a surjection has a right inverse and only

a bijection has inverses. The inverse of f is often written

as f with a -1 superscript.