We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
83
1
avatar+45 

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+102461 
+1

\(f(x) = \lfloor x\rfloor - x\)

 

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

6 Online Users

avatar
avatar