Let f(x)=ln(x). Find the domain of the function g(x)=f(e−f(x))

Answer 1

e^-f(x) = e^-lnx = 1/x
so, g(x) = ln(1/x) = -lnx = -f(x)

Answer 2

(0, e^e)? or is it just (0,e)?