Final answer:
With the provided information, we cannot determine if x = 4 is a root of f(x), as the specific equation for f(x) is not given. Techniques like using the quadratic formula or taking roots are mentioned, but cannot be applied without the actual equation of f(x).
Step-by-step explanation:
To determine if x = 4 is a root of the function f(x), we should substitute x with 4 in the given equation and check if the resulting statement is true. If we have a quadratic equation of the form ax²+bx+c = 0, the roots of this equation can be found using the quadratic formula. Unfortunately, the information provided is incomplete and does not give a specific equation for f(x). Therefore, with the given data, we cannot conclusively say whether x = 4 is a root of f(x) since we do not have the full equation for f(x).
The references to concepts like taking the square root or the fourth root and complete the square suggest that we might need to use these techniques to work with quadratic equations, or to solve equations involving powers, but without a specific equation of f(x), these techniques cannot be applied. Even for the provided equation (2x)² = 4.0 (1 − x)², which can be solved for x, we cannot assume this is f(x) without proper context.