Question

f(x) = 4x² + 5x – 3g(x) = 4x³ – 3x² + 5Find (f - g)(x).A. (f - g)(x) = 4x³ + x² + 5x + 2B. (f - g)(x) = 4x³ – 7x² – 5x + 8C. (f - g)(x) = -4x³ + x² + 5x + 2D. (f - g)(x) = -4x³ + 7x² + 5x – 8

Answer 1

Given the following functions:

f(x) = 4x² + 5x – 3

g(x) = 4x³ – 3x² + 5

Finding (f-g)(x) means f(x) - g(x).

We get,

$\text{ (f-g)(x) = f(x) - g(x)}$$\text{f(x) - g(x) = (}4x^{2}+5x-3)\text{ - (}4x^{3}-3x^{2}+5)$$\text{= }4x^2+5x-3\text{-}4x^3+3x^2-5$$\text{= -}4x^3+4x^2+3x^2+5x-3-5$$\text{= -}4x^3+7x^2+5x-8$

Therefore, the answer is letter D. (f - g)(x) = -4x³ + 7x² + 5x – 8