Given f:X->Y, the image of x is f(x). The preimage of y is then f^(-1)(y)={x|f(x)=y}, or all x whose image is y. 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.

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