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Vs: image: the codomain is the set that the function might reach.
The image is the exact set that it actually reaches.
E.g. the function:
could have:
  • codomain
  • image
Note that the definition of the codomain is somewhat arbitrary, e.g. could as well technically have codomain:
even though it will obviously never reach any value in .
The exact image is in general therefore harder to characterize.