Question

Let f(x) = 3x³ - 4x² + 5x - 18 and g(x) = x - 2. Which statement is true regarding operations on these two functions?

A) f(x) x g(x) = 4x⁴ - 9x³ + 14x² - 27x + 36
B) f(x)/g(x) = 3x² + 2x + 9, x doesn't equal 2
C) f(x) - g(x) = 2x³ - 6x² + 5x - 18
D) f(x) + g(x) = 3x³ - 4x² + 6x - 16

Answer 1

The accurate operation on the functions f(x) and g(x) is f(x) - g(x) = 3x³ - 4x² + 4x - 16, which is obtained by subtracting g(x) from f(x).

Step-by-step explanation:

The correct statement regarding operations on the functions f(x) and g(x) is option C) f(x) - g(x) = 3x³ - 4x² + 3x - 16. This is because when you subtract g(x) from f(x), you are effectively subtracting (x - 2) from each term in f(x). Mathematically, this subtraction should be per the following:

f(x) - g(x) = (3x³ - 4x² + 5x - 18) - (x - 2)

This simplifies to:

3x³ - 4x² + 5x - 18 - x + 2 = 3x³ - 4x² + 4x - 16

Therefore, the correct statement regarding the operations on f(x) and g(x) is D) f(x) + g(x) = 3x³ - 4x² + 6x - 16.