Final Answer:
The function (-2f)(x) is equal to -2(x² + 4), which simplifies to -2x² - 8. The domain of (-2f)(x) is all real numbers, denoted as (-∞, ∞).
Step-by-step explanation:
To find (-2f)(x), we multiply the original function f(x) = x² + 4 by -2. Therefore, (-2f)(x) = -2(x² + 4). Distributing the -2 to both terms inside the parentheses gives us -2x² - 8.
Now, let's consider the domain of (-2f)(x). In mathematics, the domain is the set of all possible input values for which the function is defined. Since the function is a polynomial, it is defined for all real numbers. There are no restrictions on the values of x for which (-2f)(x) is valid.
In interval notation, the domain of (-2f)(x) is expressed as (-∞, ∞), indicating that x can take any real value from negative infinity to positive infinity. This reflects the fact that the quadratic function and its scalar multiplication by -2 are defined for the entire real number line. Therefore, (-2f)(x) is a valid function for all real values of x.