Answer
a) $D=\{x|x \in (e,\infty)\},$
b) $e^{e^{e^x}}=y=f^{-1}(x)$
Work Step by Step
We are given:
$f(x)=\ln(\ln (\ln x))$.
a) To find the domain of $f(x)$.
for $\{x|\ln (\ln x) \gt 0\}=\{x|\ln x\gt 1\} =\{x|x\gt e^1\}=(e,\infty)$.
b) The Inverse of $f(x),$ $f^{-1}(x)$ is.
$y=\ln(\ln (\ln x)),$
$x=\ln(\ln (\ln y)),$
$e^x=\ln (\ln y),$
$e^{e^x}=\ln y,$
$e^{e^{e^x}}=y=f^{-1}(x)$
