How do you find the inverse of #f(x)= 1- ln(x-2)#?

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Answer 1 · 2018-03-11T05:08:44

The inverse of #f(x)# is #e^(1-x)+2#

First, we take our function #f(x)=y#:

#y=1-ln(x-2)#

Then switch the variables:

#x=1-ln(y-2)#

Solve for #y#.

#ln(y-2)=1-x#

Remember that for any #e^x=b,# we take that #lnb=x#. Here:

#y-2=e^(1-x)#

#y=e^(1-x)+2#

The inverse of #f(x)# is #e^(1-x)+2#