Given the polynomial functions, find the product function and the specified value.
-Let $f ( x ) = x + 3$ and $g ( x ) = x ^ { 2 } - 9 x - 7$. Find $( f g ) ( x )$ and $( f g ) ( - 4 )$.
A) $( f g ) ( x ) = 3 x ^ { 3 } + 27 x ^ { 2 } - 21 x ; ( f g ) ( - 4 ) = - 540$
B) $( f g ) ( x ) = x ^ { 3 } + 12 x ^ { 2 } + 34 x + 21 ; ( f g ) ( - 4 ) = 285$
C) $( f g ) ( x ) = x ^ { 3 } - 6 x ^ { 2 } - 34 x - 21 ; ( f g ) ( - 4 ) = - 45$
D) $( \mathrm { fg } ) ( \mathrm { x } ) = \mathrm { x } ^ { 3 } - 9 \mathrm { x } ^ { 2 } - 7 \mathrm { x } ; ( \mathrm { fg } ) ( - 4 ) = - 180$

Question

Quizplus · Accepted Answer

The product function $(fg)(x)$ is obtained by multiplying $f(x) = x + 3$ and $g(x) = x^2 - 9x - 7$, resulting in $x^3 - 6x^2 - 34x - 21$. Evaluating this at $x = -4$ gives $(fg)(-4) = -45$.

Given the Polynomial Functions, Find the Product Function and the Specified