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!

Absolute value

  1. Oct 3, 2008 #1
    1. The problem statement, all variables and given/known data
    Rewrite the following expressions without absolute value signs, treating various cases separately where neccesary

    2. Relevant equations

    the question is do i have 2 answers to this ?
  2. jcsd
  3. Oct 3, 2008 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Yes there will be two cases. At first inspection one might conclude that there would be four cases, but you should note that one of the absolute functions is not necessary.
  4. Oct 3, 2008 #3


    User Avatar
    Staff Emeritus
    Science Advisor

    There is only one[/b\] function for this, which may have different parts.

    If f(x)= a- |a- |x||, then, of course, you need to look at x< 0 and x> 0, then at the cases |x|> a and |x|< a.

    You could also write this as a single "formula" using the Heaviside step function which is defined as H(x)= 0 if x< 0, H(x)= 1 if [itex]x\ge 0[/itex].
  5. Oct 3, 2008 #4
    why would there be 4 cases ?
  6. Oct 3, 2008 #5


    User Avatar
    Staff Emeritus
    Science Advisor

    Hmmm, the function is a-|a- |x||. If x> 0 that is a- |a- x| so if x< a, that is if a-x> 0, we have a- (a- x)= x. If x> a, that is if a- x< 0, |a-x|= -(a-x) and we have a+(a-x)= 2a- x.

    If x< 0, so we have a- |a+ x|. Now if a> -x, so x+ a> 0, that is a- (a+ x)= -x. Finally if a< -x so x+ a< 0, that is a+ (a+x)= 2a+ x. Looks like 4 cases to me.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Absolute value
  1. Absolute Values (Replies: 5)

  2. Absolute value (Replies: 3)

  3. Absolute value (Replies: 4)

  4. Absolute values (Replies: 5)

  5. Absolute value (Replies: 2)