Final answer:
The domain of the composition function f(g(x)) when f(x) = x²/³ and g(x) = x¹² is all real numbers, because both the individual functions f and g are defined for all real values, with no restrictions.
Step-by-step explanation:
The question asks us to find the domain of the composition function when f(x) = x²/³ and g(x) = x¹². The domain of a function is the set of all possible input values (x-values) for which the function is defined. In this case, since the original functions involve powers of x, we must consider if there are any restrictions due to these operations. For f(x), as a cubic root of a square (x²/³), all real numbers are acceptable because every real number has a real cubic root. Therefore, the domain for f(x) is all real numbers. The function g(x) is simply a power of 12, which also has no restriction across the real numbers. Thus, the domain for the composition f(g(x)) will be all real numbers as well, since it's the domain of f(x) that matters in this composition.