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Definition (Image Of A Function)
Let $f:X\to Y$. The image of $f$ is the set $f(X)$.
Some people call the image of $f$ the "range of $f$", while other people use the word "range" to denote the codomain. The word "range" is unfortunately dependent on author. For this reason, we'll stick to the words "codomain" and "image" to separate these two different sets.