$(2)$ a$)10pts$ Find the domain of the function

$f(x)=(1-|1-|3-|x-2|||{)}^{\frac{1}{4}}$

b$)10pts$ Let $f(x)=x^2+1$ and $g(x)=\frac{1}{\sqrt[\phantom{2}]{lnx-1}}.$ Find $f$@$g$ and $g$@$f$ and their domains.