Domain of composite function

Question

g(x)=sqrt x + 2 ,k(x)=1/(x-3)

Find the domain of g(k(x)).

Answer 1

g(x) = sqr(x) +2, k(x)=1/(x-3)

g(k(x))= sqr(1/(x-3)) +2

domain is x>3

since x=3 is undefined

and x<3 creates an imaginary number