i $\displaystyle f$ is a bijection function from X-->X
prove
f inverse(f(x)) = x
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.