Inverse Image
"Preimage" redirects here. For the cryptographic attack on hash functions, see preimage attack.Let f be a function from X to Y. The preimage or inverse image of a set B ⊆ Y under f is the subset of X defined by
The inverse image of a singleton, denoted by f −1 or by f −1, is also called the fiber over y or the level set of y. The set of all the fibers over the elements of Y is a family of sets indexed by Y.
Again, if there is no risk of confusion, we may denote f −1 by f −1(B), and think of f −1 as a function from the power set of Y to the power set of X. The notation f −1 should not be confused with that for inverse function. The two coincide only if f is a bijection.
Read more about this topic: Image (mathematics)
Famous quotes containing the words inverse and/or image:
“Yet time and space are but inverse measures of the force of the soul. The spirit sports with time.”
—Ralph Waldo Emerson (1803–1882)
“I have often thought that if photography were difficult in the true sense of the term—meaning that the creation of a simple photograph would entail as much time and effort as the production of a good watercolor or etching—there would be a vast improvement in total output. The sheer ease with which we can produce a superficial image often leads to creative disaster.”
—Ansel Adams (1902–1984)