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Illustration Example of the Image Set of a Function

Example of the Image Set of a Function
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An example of a domain \(\mathbb{X}\) and a codomain \(\mathbb{Y}\) is shown. Also, a function \(f\) is constructed which assigns to all elements \(x\) in \(\mathbb{X}\) a \(y\) element in \(\mathbb{Y}\). The image set \(\mathbb{im}(f)\) is a set that contains all \(y\) elements that have been assigned an \(x\) element. So in the example the image contains the following elements:\[ \mathbb{im}(f) ~=~ \{ 10, 42, 2 \} \]