Question

Find ( f - g)(x).

f (x) = -2x2 - 2x - 3 and g(x) = 3x2 - 4x - 4

Answer 1

`\large\boxed{(f-g)(x)=-5x^2+2x+1}`

Explanation:

`(f-g)(x)=f(x)-g(x)\\\\\text{We have}\ f(x)=-2x^2-2x-3\ \text{and}\ g(x)=3x^2-4x-4.\\\\\text{Substitute:}\\\\(f-g)(x)=(-2x^2-2x-3)-(3x^2-4x-4)\\\\(f-g)(x)=-2x^2-2x-3-3x^2+4x+4\qquad\text{combine like terms}\\\\(f-g)(x)=(-2x^2-3x^2)+(-2x+4x)+(-3+4)\\\\(f-g)(x)=-5x^2+2x+1`