Question

Domain of f(x)=3x+6,g(x)=x+1

Answer 1

Here you have shared two separate functions, f(x) and g(x).  You have not indicated how f and g interact.  Is g supposed to be the input to f?  or what?

The domains of f and g are "the set of all real numbers."

If you meant "find the domain of f(g(x))," then we're finding the domain of 
3(x+1)+6, which happens to be the same as before:  "the set of all real numbers."

Kindly check to ensure that you have shared ALL of the given problem.