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Notation for image and preimage

Is there a standard notation for the function $F$?

$f:X\to Y$, define $F:2^X \to 2^Y$ as $F(S) = \{f(x)|x\in S\}$.

Recently I have to define this kind of function very often, and wonder there are already notations for this.

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    Maybe a modified version of Brian's suggestion: ${_2}f$...maybe chemists prefer this one.2012-06-19

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