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
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.