If f(x) = –4x2 – 6x – 1 and g(x) = –x2 – 5x + 3, find (f – g)(x).

(f – g)(x) = -3x² - x -4.

Step-by-step explanation:

Given : If f(x) = –4x² – 6x – 1 and g(x) = –x²– 5x + 3.

To find :  (f – g)(x).

Solution ; We have given that  f(x) = –4x² – 6x – 1

g(x) = –x²– 5x + 3.

(f – g)(x) = f(x) - g(x).

(f – g)(x) = (–4x² – 6x – 1 ) - ( –x²– 5x + 3) .

(f – g)(x) = –4x² – 6x – 1 + x²+ 5x - 3 .

Combine like terms

(f – g)(x) = –4x² +  x² - 6x + 5x -1 -3.

(f – g)(x) = -3x² - x -4.

Therefore,  (f – g)(x) = -3x² - x -4.