The range of the function f(x) = [x] - x is | vedclass

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Question

(B) The function is defined as $f(x) = [x] - x$,where $[x]$ denotes the greatest integer function.We know that for any real number $x$,$x = [x] + \{x\

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$(-1, 0]$

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(B) The function is defined as $f(x) = [x] - x$,where $[x]$ denotes the greatest integer function.We know that for any real number $x$,$x = [x] + \{x\}$,where $\{x\}$ is the fractional part of $x$.Therefore,$[x] - x = -\{x\}$.The fractional part function $\{x\}$ takes values in the interval $[0, 1)$.Thus,$-\{x\}$ takes values in the interval $(-1, 0]$.Hence,the range of the function $f(x) = [x] - x$ is $(-1, 0]$.

The range of the function $f(x) = [x] - x$ is

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