Final answer:
To find f(x) - g(x), subtract the function g(x), which after simplification is -7x² - 7x, from the function f(x), -3x² - 4x + 4. The result is 4x² + 3x + 4, making the correct choice d. f(x) - g(x).
Step-by-step explanation:
To find the expression equal to f(x) - g(x), we first need to define each function separately and then perform the subtraction. The function f(x) is given as f(x) = -3x² - 4x + 4, and the function g(x) is defined as g(x) = x(-7x - 7), which simplifies to g(x) = -7x² - 7x. Now, to find f(x) - g(x), we subtract g(x) from f(x):
f(x) - g(x) = (-3x² - 4x + 4) - (-7x² - 7x)
Distributing the negative sign through the parentheses, this becomes:
f(x) - g(x) = -3x² - 4x + 4 + 7x² + 7x
Combining like terms, we arrive at:
f(x) - g(x) = 4x² + 3x + 4
The correct choice is d. f(x) - g(x), with the resulting expression being 4x² + 3x + 4.