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

Jul 2, 2016

$x > {e}^{- 3} > 0.0497871$, nearly..
$x = 0.0497871 \left({e}^{{e}^{f}}\right)$, nearly

#### Explanation:

For f to be real,

$3 + \ln x > 0$. So,$\ln x \succ 3$. And so, $x > {e}^{- 3} > 0.0497871$, nearly.

Inversion:

${e}^{f} = 3 + \ln x .$

$S o , \ln x = {e}^{f} - 3.$

And so, $x = {e}^{{e}^{f} - 3} = {e}^{- 3} {e}^{{e}^{f}} = 0.0497871 {e}^{{e}^{f}}$