Question

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

Answer 1

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]}