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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