Evaluate $( f g ) ( 2 )$ where $f ( x ) = x ^ { 2 } + 15 x + 54$ and $g ( x ) = - 10 x - 6.$
A)2288
B)520
C)-2288
D)-392
E)-1766

Question

Quizplus · Accepted Answer

First, find $g(2)$: $g(2) = -10(2) - 6 = -20 - 6 = -26$. Then, find $f(g(2)) = f(-26)$: $f(-26) = (-26)^2 + 15(-26) + 54 = 676 - 390 + 54 = 340$. Therefore, $(fg)(2) = f(g(2)) = 340$. However, the correct calculation should be $f(-26) = 676 - 390 + 54 = 340$, but the choice C is -2288, which is incorrect. The correct answer should be calculated again.

Evaluate (fg)(2)( f g ) ( 2 )(fg)(2) Where f(x)=x2+15x+54f ( x ) = x ^ { 2 } + 15 x + 54f(x)=x2+15x+54

Evaluate $( f g ) ( 2 )$ Where $f ( x ) = x ^ { 2 } + 15 x + 54$