Evaluate the indicated function for $f ( x ) = x ^ { 2 } + 6$ and $g ( x ) = x - 5$ . $( f / g ) ( - 4 ) - g ( 6 )$
A) $- \frac { 5 } { 26 }$
B) $- \frac { 31 } { 9 }$
C) $- \frac { 9 } { 13 }$
D) $- \frac { 13 } { 9 }$
E) $- \frac { 9 } { 31 }$

Question

​​​Evaluate the indicated function for $f ( x ) = x ^ { 2 } + 6$ and $g ( x ) = x - 5$ .​ $( f / g ) ( - 4 ) - g ( 6 )$ ​ ​
A) $- \frac { 5 } { 26 }$
B) $- \frac { 31 } { 9 }$
C) $- \frac { 9 } { 13 }$
D) $- \frac { 13 } { 9 }$
E) $- \frac { 9 } { 31 }$

Quizplus · Accepted Answer

First, calculate $f(-4) = (-4)^2 + 6 = 16 + 6 = 22$ and $g(-4) = -4 - 5 = -9$. So, $(f/g)(-4) = f(-4)/g(-4) = 22 / (-9) = -22/9$. Then, calculate $g(6) = 6 - 5 = 1$. Finally, $(f/g)(-4) - g(6) = -22/9 - 1 = -22/9 - 9/9 = -31/9$.

​​​Evaluate the Indicated Function For f(x)=x2+6f ( x ) = x ^ { 2 } + 6f(x)=x2+6

Evaluate the Indicated Function For $f ( x ) = x ^ { 2 } + 6$