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Definition (Preimage Or Inverse Image)
If $f:A\to B$ and $C\subseteq B$, then the preimage of $C$ under $f$ is the set of all $a\in A$ such that $f(a)\in C$, and we write the preimage of $C$ under $f$ as $$f^{-1}(C)=\{a\in A\mid f(a)\in C\}.$$ When $C=\{c\}$ contains a single element, we often write the preimage of $C$ under $f$ as $f^{-1}(c)$ instead of using the more formal cumbersome notation $f^{-1}(\{c\})$.
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