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I am given the piecewise function $f: \mathbb{Z} \to \mathbb{Z},$ $ f(x) =\left\{ \begin{matrix} 2n, & \text{if }n \text{ is even} \\ n, & \text{if }n \text{ is odd} \end{matrix}\right.$

I need to find the image of this function. So far I have tried plotting out a list of points, but I am unable to find a pattern. Is there a better approach to this problem?

wzbillings
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  • You have a piecewise function, so begin by focusing only on one piece at a time. For instance, what's the image of $f$ under the set of odd integers? – John Griffin Nov 09 '17 at 04:06
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    So $\text{im}(f)$ contains all odd integers, as well as all integer multiples of 4. But how do I express that as one set? Do I just say ${n \mid n $ is odd, or $ n=4t, t \in \mathbb{Z} }$? – wzbillings Nov 09 '17 at 04:11
  • Exactly @jeanquilt. – TRUSKI Nov 09 '17 at 04:45

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