Final answer:
The difference of the functions (f-g)(x) = -12x^2 - 8x + 9, and when evaluated at x = -4, (f-g)(-4) = -151.
Step-by-step explanation:
The question asks to find the difference of two functions, (f-g)(x), and then to evaluate this difference for x = -4.
To find (f-g)(x), we subtract the function g(x) from function f(x).
Given that f(x) = −9x^2 −2x and g(x) = −3x^2 + 6x −9, we can write:
(f - g)(x) = f(x) - g(x)
= (−9x^2 −2x) - (−3x^2 + 6x −9).
To simplify, distribute the negative sign and combine like terms:
(f - g)(x) = −9x^2 −2x - −3x^2 - 6x + 9
= −12x^2 −8x + 9.
To find (f-g)(−4), substitute -4 into the simplified expression:
(f - g)(−4) = −12(-4)^2 −8(-4) + 9
= −12(16) + 32 + 9
= −192 + 32 + 9
= −151.