1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Examine the continuity of this absolute value function

  1. Aug 19, 2014 #1
    1. The problem statement, all variables and given/known data

    y = 1-abs(x) / abs(1-x)

    3. The attempt at a solution

    For x < 0, abs(x) = -x

    y = (1+x) / -(1-x)
    = -(1+x)/(1-x)

    I stopped here because this is the part I got wrong. For x < 0, my solutions manual got (1+x) / (1-x).
    What did I do wrong?
     
  2. jcsd
  3. Aug 19, 2014 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    For ##x<0##, ##-x>0## so ##1-x>0## so ##|1-x|=1-x##. No minus sign needed in the denominator.
     
  4. Aug 19, 2014 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    For your written function
    [tex] y = 1 - \frac{|x|}{|1-x|} [/tex]
    you have ##y = 1 + x/(1-x) = 1/(1-x) ## for ##x < 0##.

    On the other hand, if you really meant something different from what you wrote, namely,
    [tex] y = \frac{1-|x|}{|1-x|} [/tex]
    then you would have ##y = (1+x)/(1-x) ## for ##x < 0##. Which function do you mean? Us parentheses for clarity, like this: y = (1-|x|)/|1-x|, or y = (1-abs(x))/ abs(1-x) if your keyboard does not have an "|" key.
     
  5. Aug 20, 2014 #4
    It was the second one: y = (1-|x|)/|1-x|. So how did you get y=(1+x)/(1−x) for x<0?
     
  6. Aug 20, 2014 #5

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Didn't you read post #2?
     
  7. Aug 20, 2014 #6
    Sorry I should have addressed your reply as well. So LCKurtz let me start off by saying what I understand from your reply.

    Since -x > 0 can be written as x < 0, therefore -(1-x) > 0 can also be written as 1-x < 0. If this is true then can't this apply to any time we need to consider the negative case for an absolute value function. For the numerator, why can't this same logic apply?
     
  8. Aug 20, 2014 #7

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Have you forgotten that -(-x) = x and that for x < 0 we have |x| = -x?
     
  9. Aug 20, 2014 #8

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I can't make any sense out of that reply. Why don't you just follow the steps I gave you? You start with ##x<0##. Multiply both sides by ##-1## so ##-x>0##. Since ##-x## is positive, adding ##1## to it is still positive, so ##1-x > 0##. The absolute value of a positive number is the number itself so ##|1-x| = 1-x##. You don't get ##-(1-x)##.
     
  10. Aug 20, 2014 #9
    My mind must have been somewhere else when I was reading your first reply. It makes crystal clear sense. Thank you for your time.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Examine the continuity of this absolute value function
Loading...