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Finding the inverse of a modulus function

  1. Dec 24, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the inverse of
    y=|x-4|


    2. Relevant equations
    -


    3. The attempt at a solution
    i tried y+4=|x|
    replacing y with x,
    x+4= |y|
    and im quite stuck because of the modulus sign.
    do i go on with x+4=y or -x-4=y?
     
  2. jcsd
  3. Dec 24, 2009 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    There is a fundamental problem here: y= |x+ 4| is NOT 'one to one' and so does NOT have an inverse! In order to have 'inverses', we would neet to separate the function at x= -4. For [itex]x\ge -4[/itex], [itex]x+ 4\ge 0[/itex] so y= x+4. The inverse of that is, of course, y= x-4 defined only for [itex]x\ge 0[/itex]. For x< -4, x+ 4< 0 so |x+4|= -(x+4)= -x- 4 so y= -x- 4. The inverse of that is y= -x- 4 again. And that, also, is defined only for [itex]x\ge 0[/itex].
     
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