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A basic function question - with a strange absolute value placement

  1. May 21, 2010 #1
    1. The problem statement, all variables and given/known data

    If f(x) is equal to...

    x+9 if x<-3
    -2x if |x|[tex]\leq[/tex] 3
    -6 if x > 3

    2. The attempt at a solution

    The first and third "segments" of when the function is defined as being x+9 and -6 are pretty straightforward to me, however I am unaware of the significance of the placement of the absolute value of x in the middle if statement of when the function is equal to -2x. Is it significant at all? Does this imply this function is undefined when -3 < x < 0? Or is it, as my initial hunch was, really just some type of a distraction?
  2. jcsd
  3. May 21, 2010 #2


    Staff: Mentor

    |x| <= 3 is equivalent to -3 <= x <= 3, so your hunch that this is a distraction is wrong.
  4. May 21, 2010 #3
    0 \le \left| x \right| \le a \; \Leftrightarrow \; -a \le x \le a
  5. May 21, 2010 #4
    Thank you. I didn't choose my word "distraction" cautiously enough. Since the statements you both posted are equivalent - that was indeed what I needed to know.
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