What is the inverse of #y=log(x-4)+2# ?

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Answer 1 · 2018-03-02T11:18:31

#10^(x-2)+4# is the inverse.

We have the function #f(x)=y=log(x-4)+2#

To find #f^-1(x)#, we take our equation:

#y=log(x-4)+2#

Switch the variables:

#x=log(y-4)+2#

And solve for #y#:

#x-2=log(y-4)#

We can write #x-2# as #log(10^(x-2))#, so we have:

#log(10^(x-2))=log(y-4)#

As the bases are the same:

#y-4=10^(x-2)#

#y=10^(x-2)+4#

Which is your inverse.