Final answer:
The domain of the composite function is all real numbers.
Step-by-step explanation:
The domain of a composite function is determined by the domain of the inner function and the values produced by the inner function that are within the domain of the outer function.
In this case, the inner function g(x) = 4x - 1 is a linear function, which means its domain is all real numbers.
Next, we need to consider the values produced by g(x) that are within the domain of f(x) = 6x^2 - 7x + 8, which is defined for a real number x. To find the values produced by g(x) within the domain of f(x), we set up the inequality 0 ≤ g(x) ≤ 20 and solve for x. It turns out that g(x) is within the desired range for all real values of x.
Therefore, the domain of the composite function (f ∘ g)(x) is all real numbers.