You can put this solution on YOUR website! f(x)=1/x is not defined when x=0 so the domain of f is Real numbers without zero
and g(x)=x+3 is defined for all values of x so the domain of g is Real numbers
f(g(x))=f(x+3)=1/(x+3) which is not defined when x=-3
so the domain of f of g is real numbers excluding -3 that is R-{-3}