image of a function

The image of a function is the set of all output value it creates.

Image of a Subset

The image of a subset in the function domain is

Inverse Image

Given a function . Let . The preimage or inverse image of under denoted by , is the subset of defined by

Despite the notation, preimage can exists even when the inverse of doesn’t. Though if does have an inverse, then the preimage is exactly the image of under inverse map, thus justifying this somewhat misleading notation. ¹

Footnotes

Footnotes

1. Pre-Image — from Wolfram MathWorld ↩