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:$\mathbb{im}(f) ~=~ \{ 10, 42, 2 \}$