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