If some [[Function]] $f$ is not [[Injective]], it is [[Lossy Function|Lossy]]. This is because once $f$ is applied to some value $x$ such that the [[Image]] is $y$, there is no way to know for certain what the original [[Pre-Image]] was. There may however be a way of finding *a* [[Pre-Image]]. >[!example] >Any [[Linear Transformation]] that maps a lower dimensional space to a higher dimensional space is [[Lossy Function|Lossy]]. > $\huge f: \R^m \to \R^n, m < n $