Final answer:
The domain of the function (f of g)(x) is all real numbers except x = 0 and x = 6.
Step-by-step explanation:
The domain of the function (f of g)(x) can be determined by finding the values of x for which the function is defined. To find the domain, we need to look at the restrictions on the individual functions f(x) and g(x), and then combine their domains. In this case, the domain of f(x) is all real numbers except x = 6 (since x - 6 cannot be equal to 0). The domain of g(x) is also all real numbers except x = 0 (since 3/x cannot be defined when x = 0).
To find the domain of (f of g)(x), we need to determine the values of x for which both f(x) and g(x) are defined. Since f(x) and g(x) have different restrictions, we need to find the intersection of their domains. In this case, the intersection is all real numbers except x = 0 and x = 6. Therefore, the domain of (f of g)(x) is all real numbers except x = 0 and x = 6.