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The function\(\lfloor x\rfloor\)is defined as the largest integer less than or equal to \(x\) . For example, \(\lfloor 5.67\rfloor = 5\)\(\lfloor -\tfrac 14\rfloor = -1\), and \(\lfloor 8 \rfloor=8\) .

What is the range of the function \(f(x) = \lfloor x\rfloor - x~\) Express your answer in interval notation

 Feb 26, 2021
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It's from (-1, 0].

 

If x is an integer, then [x] - x = 0.

 

If x is a decimal, then [x] - x is the negative of the fractional part of x.

 Feb 26, 2021

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