Finding the inverse of a modulus function

[rreedde]

Homework Statement

Find the inverse of
y=|x-4|

Homework Equations

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The Attempt at a Solution

i tried y+4=|x|
replacing y with x,
x+4= |y|
and I am quite stuck because of the modulus sign.
do i go on with x+4=y or -x-4=y?

 

[HallsofIvy]

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 $x\ge -4$, $x+ 4\ge 0$ so y= x+4. The inverse of that is, of course, y= x-4 defined only for $x\ge 0$. 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 $x\ge 0$.