For example, if I define a function $f(x) = -x$ with a domain and codomain of positive numbers (in other words a nonexistant image and preimage) would this still be a function?
2026-03-24 23:44:27.1774395867
Can the image and preimage of a function be the empty set?
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No, it is not a function.
In particular $f(1)$ is not well-defined as the rule maps outside the codomain. It does not have exactly one output.