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Define $\{x\} = x-\lfloor x \rfloor$. That is to say, $\{x\}$ is the "fractional part" of $x$. For example, if you were to expand a positive number $x$ as a decimal, $\{x\}$ is the stuff after the decimal point. For example $\left\{\frac{3}{2}\right\} = 0.5$ and $\{\pi\} = 0.14159\dots$ Now, using the above definition, determine if the function below is increasing, decreasing, even, odd, and/or invertible on its natural domain: $$f(x) = \lfloor x \rfloor - \left\{ x \right\}$$ For each property, write inCreasing, Decreasing, Even, Odd, inVertible in that order (alphabetical).

 

Please include the answer and an explanation if possible.

 Aug 4, 2021
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The answer is DOV.

 Sep 19, 2021

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