Domain

\(\sqrt{1-\sqrt{2+\sqrt{3+\sqrt{x}}}} \)

Note   that  even if x =  0   (as small as it  can  be),,,we have

1 - sqrt [ 2 + sqrt (3) ]   which is less than   0......so the quantity under the radical isn't real

If x >  0     then    sqrt [ 2 + sqrt (3 + sqrt (x)) ]    will still be >1  which makes the quantity under the radical still < 0] 

So.....this  can't have a domain of real numbers