What is the inverse function of # f(x)=3+sqrt(x-8)#?

1 Answer
Alan P.
May 27, 2015

(Because I find it easier to work with, I am replacing #f(x)# with #y#

Given #y = 3+sqrt(x-8)#

We want to write an equivalent relationship of the form
#x = # and expression in terms of #y#

#y = 3+sqrt(x-8)#

#sqrt(x-8) = y-3#

#x-8 = y^2-6y+9#

#x = y^2 -6y +17#

It is possible to verify that this is the inverse of the given equation by plugging #3+sqrt(x-8)# into #x=y^2-6y+17# in place of #y#.
The result (after simplifying) will be #x=x#

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