Final answer:
The largest x that is not in the domain of g(x) = f(f(x)), given that f(x) = 1/x - 3, is 1/3 because it makes the denominator zero after the first application of f, resulting in an undefined value for g(x).
Step-by-step explanation:
To find the largest x that is not in the domain of g(x) = f(f(x)), where f(x) = 1/x - 3, we need to consider when the function f(x) is undefined. The only time the function 1/x is undefined is when x is 0 since division by zero is not allowed. However, for the composition g(x), we must also consider when the inside function, f(x), would result in 1/0 after applying f again. For f(x) to give 0, we solve the equation 1/x - 3 = 0. This gives x = 1/3. Therefore, the largest x that is not in the domain of g(x) is 1/3 because when x = 1/3, the denominator of the inside function becomes zero after the first application of f, making the second application undefined.