# functions

• July 18th 2009, 09:26 AM
doresa
functions[SOLVED]
i $f$ is a bijection function from X-->X
prove
f inverse(f(x)) = x
• July 18th 2009, 03:56 PM
AlephZero
If $f : A \rightarrow B$ is an injective function, then the inverse is defined by

$f^{-1}(y)=x \iff f(x)=y$ for all $y \in B.$

Since bijective implies injective, the result follows immediately.