How do you find the inverse of #y = - |x-3| + 5#?

1 Answer
Alan P.
Jun 22, 2017

#y=8-xcolor(white)("xxx")andcolor(white)("xxx")y=x-2#
Note that the "inverse" is not a (single-valued) function.

Explanation:

Given #y=-abs(x-3)+5#
#{: ("if",x >=3,color(white)("XXX"),"if",x < 3), (rarr,y=-(x-3)+5,,rarr,y=3-x+5), (rarr,y=x-2,,rarr,y=8-x), (rarr,x=y+2,,rarr,x=8-y), ("Noting",,,,), (,x>=3,,,x<3), (,rarr y<=5,,,y<5) :}#

Exchanging the #x# and #y# variables to give the "inverse":
#{: (color(white)("xxx"),y=x+2,color(white)("XXX"),y=8-x), ("with",,x<=5,) :}#

This makes sense if you consider the graph of #-abs(x-3)+5#
enter image source here

Consider any horizontal line (which will provide the inverse values).
The inverse can not have Domain values in excess of #5#
and for every value #<5#, the #2# values are provided for the Range.

Related questions
See all questions in Absolute Value Equations
Impact of this question
1247 views around the world
You can reuse this answer
Creative Commons License