Composite function

So composition function is s(x) = ln(ln(x)) and natural domain is (1, +infinity)
So s(s(x)) = s(ln(ln(x)) = ln(ln(ln(ln(x)))) .
Is natural domain this function also (1,+infinity)????
What is the axes intercepts of y = s(s(x)) ???
I have tried assign x = 0 but my calculator can not find any solution .

Thank you.

The function does not have a y-intercept since when x = 0, ln(x)=ln(0) is undefined.

If you do set y = 0 to find the x-intercept then, then

As for the domain, the domain will be from to infinity.