Given , the image of is . The preimage of is then , or all whose image is . Images are elements of the range, while preimages are subsets (possibly empty) of the domain.
Portions of this entry contributed by Todd Rowland
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Rowland, Todd and Weisstein, Eric W. "Preimage." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Preimage.html