Answer
a) $D=\{x|x \in (1,\infty)\}$.
b) $10^{2^x}=y=f^{-1}(x)$
Work Step by Step
We are given:
$f(x)=\log_{2}({\log_{10}x})$.
a) To find the domain of $f(x)$.
for $\{x|(\log_{10}x) \gt 0\}=\{x|x\gt 10^0\} =\{x|x\gt1\}=(1,\infty)$.
b) The Inverse of $f(x),$ $f^{-1}(x)$ is.
$y=\log_{2}(\log_{10}x),$
$x=\log_2(\log_{10}y),$
$2^x=\log_{10} y,$
$10^{2^x}=y=f^{-1}(x)$
