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.

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