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1.) 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.
 

 

 

 

 

\(\text{Problem (with }\LaTeX)\)

 

 

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.

 Apr 27, 2019
edited by lolzforlife  Apr 28, 2019
edited by lolzforlife  Apr 28, 2019
 #1
avatar+107060 
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\(f(x) = \lfloor x\rfloor - x\)

 

The floor of x is less then or equal to x with a difference of less than 1 

So the subtraction will result in a number between -1 and 0

 

The range is     (-1,0]

 May 1, 2019

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