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Range of a f(x) involving floor

  1. Mar 12, 2009 #1
    1. The problem statement, all variables and given/known data
    I have to find the range of f(x) where:
    f(x)=7*floor(x) - floor(7*x)
    x is a real number.

    Then I have to prove that this set of numbers is correct.


    3. The attempt at a solution
    I am still on the range part, and thus am only asking about that part at the moment. It seems to me that the range of f(x) would be (-infinity,+infinity). Is there a reason that it wouldn't be?
     
  2. jcsd
  3. Mar 12, 2009 #2
    Sketch the graphs of g(x) = 7*floor(x) and h(x) = floor(7x) on the same paper.
     
  4. Mar 12, 2009 #3
    Ah yes, back to basics for me.

    Ok so it seems that all possible values of f(x) are:
    -6,-5,-4,-3,-2,-1,0;

    thus range of f(x) = (-6,0).

    Correct?
     
    Last edited: Mar 12, 2009
  5. Mar 12, 2009 #4
    what does that round thing at the end of question #4 a and #4 b mean sneakyArab
     
  6. Mar 12, 2009 #5
    seems I've found a classmate.

    I'm not sure if you mean the last symbol or next to last, so after the equation it reads:

    "is not rational"


    so its not a rational number.
     
  7. Mar 12, 2009 #6
    I think I have a working proof on this one now. Thanks for getting me started Slider!
     
  8. Mar 12, 2009 #7
    thanks man it looks all crazy i couldnt figure it out
    good luck and thanks again
     
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