I'm doing an intro course on set theory and have the question if the inverses of the surjective functions in the sets $A=\{a, b\}$ and $B= \{c, d, e\}$ are also functions.
So far, I thought that the inverse of a function $f(x)$ for example, is $f^{-1}(y)$, meaning that every function also has an inverse (which is also a function).
Given that this would make the question rather redundant, I'm not quite sure in my assumption anymore, so I would be glad if someone could verify or falsify (and explain it properly) it.
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