Given the polynomial functions, find the product function and the specified value.
-Let $f ( x ) = x + 6$ and $g ( x ) = x - 11$. Find $( f g ) ( x )$ and $( f g ) ( 2 )$.
A) $( f g ) ( x ) = x ^ { 2 } - 5 x - 66 ; ( f g ) ( 2 ) = - 72$
B) $( f g ) ( x ) = x ^ { 2 } + 5 x - 66 ; ( f g ) ( 2 ) = - 52$
C) $( \mathrm { fg } ) ( \mathrm { x } ) = \mathrm { x } ^ { 2 } + 17 \mathrm { x } + 66 ; ( \mathrm { fg } ) ( 2 ) = 104$
D) $( \mathrm { fg } ) ( \mathrm { x } ) = \mathrm { x } ^ { 2 } - 5 \mathrm { x } + 66 ; ( \mathrm { fg } ) ( 2 ) = 60$

Question

Quizplus · Accepted Answer

To find $(fg)(x)$, multiply $f(x) = x + 6$ and $g(x) = x - 11$, which gives $x^2 - 5x - 66$. Substituting $x = 2$ into this expression yields $(2)^2 - 5(2) - 66 = 4 - 10 - 66 = -72$.

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