How do you find the inverse of #f(x) = 3log(x-1)#?

1 Answer
Gió
Jul 19, 2015

I found: #f(x)=1+10^(x/3)#

Explanation:

I am not sure it is the "formal" way to do it but I do it like this:
I try to "extract" #x#:
#log(x-1)=(f(x))/3#
assuming base #10# for the log, I can write:
#x-1=10^(f(x)/3)#
#x=1+10^(f(x)/3)#
now I switch #x# and #f(x)# to get:
#f(x)=1+10^(x/3)#
Graphically:
#f(x)=3log(x-1)#
graph{3log(x-1) [-10, 10, -5, 5]}
and:
#f(x)=1+10^(x/3)#
graph{1+10^(x/3) [-10, 10, -5, 5]}

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