Final answer:
The domain of (fog)(x) is all real numbers except x = 0.
Step-by-step explanation:
The function (fog)(x) is obtained by plugging in the function g(x) into the function f(x). So, we have (fog)(x) = f(g(x)).
First, let's determine the domain of g(x). The function g(x) is defined as g(x) = 2/x. Since division by zero is undefined, we cannot have x = 0. Therefore, the domain of g(x) is all real numbers except x = 0.
Now, let's plug g(x) into f(x) to find the domain of (fog)(x). We have (fog)(x) = f(g(x)) = f(2/x) = 1/(2/x)^3 = 1/(8/x^3) = x^3/8.
Since x^3/8 is defined for all real numbers except x = 0 (which is already excluded from the domain of g(x)), the domain of (fog)(x) is all real numbers except x = 0.