Given the right context, this keeps the notation light and usually does not cause confusion. But if needed, an alternative [5] is to give explicit names for the image and preimage as functions …

This shows that the preimage of a set containing a single element is a set that may contain zero, one, two or even more elements. Indeed, it is not hard to construct an example in which the …

Dec 3, 2025 · Images are elements of the range, while preimages are subsets (possibly empty) of the domain.

Preimage, we go from a subset of our codomain, and we say what subset of our domain maps into that subset of our codomain? Now let me ask you an interesting question, and this is kind …

Jun 15, 2025 · Explore the concept of preimage in set theory, its definition, and its significance in various mathematical disciplines.

In other words, the preimage of an element \ (b\) is the set of all elements of \ (A\) that have \ (b\) as an output. Note that for preimages we use square brackets “ [,]” around the argument \ (b\) …

Similarly, the preimage of a subset $B' \subseteq B$ under $f$ is the set of all $a \in A$ such that $f (a) = b$ for some $b \in B'$. The preimage is denoted as $f^ {-1} (B')$.

2 days ago · preimage (plural preimages) (mathematics) For a given function, the set of all elements of the domain that are mapped into a given subset of the codomain; (formally) given …

Discover how Preimage powers a wide range of industries—from construction and interior design to property digitization and visual documentation. Our versatile platform adapts seamlessly to …

Put simply, the preimage of an element $ y $ in the codomain $ Y $ consists of all those values in the domain $ X $ which, when passed through the function $ f (x) $, yield $ y $ as output.