WARNING: \(f\inv(y)\) is not an inverse function! Inverse functions only exist for bijections, but \(f\inv(y)\) is defined for any function \(f\text{.}\) The point: \(f\inv(y)\) is a set, not an element of the domain. This is just sloppy notation for \(f\inv(\{y\})\text{.}\) To help make this distinction, we would call \(f\inv(y)\) the complete inverse image of \(y\) under \(f\). It is not the image of \(y\) under \(f\inv\) (since the function \(f\inv\) might not exist).
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