Inverse image

Definition: Inverse image. Let be a function, and be a subset of the codomain of . Then the inverse image (also know as the preimage) of under , denoted as , consists of those elements such that . Example: Let be the (non-invertible) mapping . The inverse image of under is

• The inverse image is very similar to the inverse of a function. It takes in the output, and gives the possible inputs
  • However, it is not a function because it also works on non-invertible (bijective) functions
    • In the example above, . There are more than 1 outputs for 1 input
  • It also takes in and returns a set