Abstract Algebra: Theory and Applications · Problem 1.12

Preliminaries — Thomas Judson

Mathematics — Abstract Algebra · functions-mappings-inverse

Problem

Let

f : X \to Y

be a bijective map. Define

f^{-1}: Y \to X

f^{-1}(y) = x

where

f(x) = y

. Show that

f^{-1}

is a bijective map and that

f^{-1} \circ f = \mathrm{id}_X

and

f \circ f^{-1} = \mathrm{id}_Y