Question

F(x)=-9x^2-2x and g(x)=-3x^2+6x-9, find (f-g)(x) and (f-g)(-4)

Answer 1

(f - g)(x)= - 6 {x}^{2} - 8x + 9

(f - g)(-4!)= - 55

Explanation:

`f(x) = - 9 {x}^(2) - 2x, \: \: g(x) = - 3 {x}^(2) + 6x - 9 \\ (f - g)(x) = f(x) - g(x) \\ = - 9 {x}^(2) - 2x - (- 3 {x}^(2) + 6x - 9) \\ = - 9 {x}^(2) - 2x + 3 {x}^(2) - 6x + 9 \\ \purple{ \boxed{ \bold{(f - g)(x)= - 6 {x}^(2) - 8x + 9}}} \\ (f - g)( - 4)= - 6 {( -4 )}^(2) - 8( - 4) + 9 \\ = - 6 * 16 + 32 + 9 \\ = - 96 + 41 \\ \red{ \boxed{ \bold{(f - g)( - 4)= - 55}}}`