Question

How do you find the domain and inverse of `f(x)=ln(3+ln(x))`?

Answer 1

`x>e^(-3)>0.0497871`, nearly..
`x=0.0497871 (e^(e^f))`, nearly

Explanation:

For f to be real,

`3+ln x>0`. So,`ln x>-3`. And so, `x>e^(-3) >0.0497871`, nearly.

Inversion:

`e^f=3+ln x.`

`So, ln x = e^f-3.`

And so, `x=e^(e^f-3)=e^(-3)e^(e^f)= 0.0497871 e^(e^f)`