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Math  /  Algebra

QuestionQuestion 9 (1 point) Evaluate the indicated function for f(x)=x2+6f(x)=x^{2}+6 and g(x)=x−5g(x)=x-5. (f/g)(−4)−g(6)(f / g)(-4)-g(6) a −526\quad-\frac{5}{26} b −913-\frac{9}{13} c −319\quad-\frac{31}{9} d −139\quad-\frac{13}{9} e −931\quad-\frac{9}{31}

Studdy Solution

STEP 1

1. We are given two functions: f(x)=x2+6 f(x) = x^2 + 6 and g(x)=x−5 g(x) = x - 5 .
2. We need to evaluate the expression (f/g)(−4)−g(6) (f / g)(-4) - g(6) .

STEP 2

1. Calculate f(−4) f(-4) .
2. Calculate g(−4) g(-4) .
3. Compute (f/g)(−4) (f / g)(-4) .
4. Calculate g(6) g(6) .
5. Evaluate the expression (f/g)(−4)−g(6) (f / g)(-4) - g(6) .

STEP 3

Calculate f(−4) f(-4) :
f(−4)=(−4)2+6 f(-4) = (-4)^2 + 6

STEP 4

Simplify f(−4) f(-4) :
f(−4)=16+6 f(-4) = 16 + 6 f(−4)=22 f(-4) = 22

STEP 5

Calculate g(−4) g(-4) :
g(−4)=−4−5 g(-4) = -4 - 5

STEP 6

Simplify g(−4) g(-4) :
g(−4)=−9 g(-4) = -9

STEP 7

Compute (f/g)(−4) (f / g)(-4) :
(f/g)(−4)=f(−4)g(−4)=22−9 (f / g)(-4) = \frac{f(-4)}{g(-4)} = \frac{22}{-9}

STEP 8

Calculate g(6) g(6) :
g(6)=6−5 g(6) = 6 - 5

STEP 9

Simplify g(6) g(6) :
g(6)=1 g(6) = 1

STEP 10

Evaluate the expression (f/g)(−4)−g(6) (f / g)(-4) - g(6) :
(f/g)(−4)−g(6)=22−9−1 (f / g)(-4) - g(6) = \frac{22}{-9} - 1

STEP 11

Simplify the expression:
(f/g)(−4)−g(6)=−229−99 (f / g)(-4) - g(6) = -\frac{22}{9} - \frac{9}{9} (f/g)(−4)−g(6)=−22+99 (f / g)(-4) - g(6) = -\frac{22 + 9}{9} (f/g)(−4)−g(6)=−319 (f / g)(-4) - g(6) = -\frac{31}{9}
The value of the expression is:
−319 \boxed{-\frac{31}{9}}

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