Consider functions f and g below.

f (x) = - 9x^2 - 7x + 12

g (x) = 3x^2 - 4x - 15

Find f (x) - g (x).

A. - 12x^2 - 11x - 3

B. 6x^2 - 11x + 27

C. - 6x^2 + 3x - 3

D. - 12x^2 - 3x + 27

Option D. - 12x² - 3x + 27

Step-by-step explanation:

The given functions are f (x) = - 9x² - 7x + 12 and g (x) = 3x² - 4x - 15

We have to find the value of f (x) - g (x)

f (x) - g (x) = (-9x² - 7x + 12) - (3x² - 4x - 15)

= - 9x² - 7x + 12 - 3x² + 4x + 15

= (-9x² - 3x²) - (7x - 4x) + 12 + 15

= - 12x² - 3x + 27

This value of f (x) - g (x) matches with option D.

Therefore, Option D. is the correct option.

D

Step-by-step explanation:

f (x) - g (x) = - 9x^2 - 7x + 12 - (3x^2 - 4x - 15) Remove the brackets

f (x) - g (x) = - 9x^2 - 7x + 12 - 3x^2 + 4x + 15

f (x) - g (x) = - 9x^2 - 3x^2 - 7x + 4x + 12 + 15

f (x) - g (x) = - 12x^2 - 3x + 27

Answer D