root(x-1/x-2{x}) , where {..} denotes fractional part .

For the function to be defined,

x-1>0 and x-2{x}>0

=> x>1 and x>=1 or x<=-1

Take the union of the two, x>1

Also, the function is defined when

x-1<0 and x-2{x}<0

=>x<1 and  -1<x<0 or 0<x<1

=> {-1<x<1} - {0}

So, the domain will be