# Finding inverse of absolute function

• Sep 25th 2009, 09:33 PM
MATHDUDE2
Finding inverse of absolute function
Hi,

I don't know/understand how to solve this inverse absolute function. The function is modeled: f(x) = |2x-5|+2

Will the inverse have both positive and negative arms? And what will the equation look like? Because when I solve for the inverse, I get f(x)=0.5(x-2)+2.5 which doesn't look right when I graph it.

Thank you!!
• Sep 25th 2009, 10:22 PM
woof
I think that you are missing part of the problem. Are the values for x restricted???

Notice that f(1)=f(4), which means that for the y value of 5, there are two x's (1 and 4) that get mapped to it. As written, this function is not 1-1, does not pass the horizontal line test, and therefore is not invertible.

However, if you restrict your domain, you can solve for an inverse. For x>=(5/2), then
f(x)=(2x-5)+2=2x-3 and you can solve for the inverse.

If you have the restriction x<=(5/2), then f(x)=-(2x-5)+2=7-2x, and you can solve for the inverse.