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\(f:\N \to \N\) defined by \(f(n) = \frac{n}{2}\text{.}\) The reason this is not a function is because not every input has an output. Where does \(f\) send 3? The rule says that \(f(3) = \frac{3}{2}\text{,}\) but \(\frac{3}{2}\) is not an element of the codomain.

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