i $\displaystyle f$ is a bijection function from X-->X

prove

f inverse(f(x)) = x

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- Jul 18th 2009, 09:26 AMdoresafunctions[SOLVED]
i $\displaystyle f$ is a bijection function from X-->X

prove

f inverse(f(x)) = x - Jul 18th 2009, 03:56 PMAlephZero
If $\displaystyle f : A \rightarrow B$ is an injective function, then the inverse is

*defined*by

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

Since bijective implies injective, the result follows immediately.