1.5k views
1 vote
Let f(x) =x^2 + x + 9 and g(x)x = -4x - 3.
Find (fg) (x) and (f/g) (x)

Let f(x) =x^2 + x + 9 and g(x)x = -4x - 3. Find (fg) (x) and (f/g) (x)-example-1
User Freeo
by
7.9k points

1 Answer

0 votes

Answer: First, we need to find the composite function (fg)(x):

(fg)(x) = f(g(x))

= f(-4x-3)

= (-4x-3)^2 + (-4x-3) + 9 (substituting g(x) into f(x))

= 16x^2 + 24x + 18

Therefore, (fg)(x) = 16x^2 + 24x + 18.

Next, we need to find the quotient function (f/g)(x):

(f/g)(x) = f(x) / g(x)

= (x^2 + x + 9) / (-4x - 3) (substituting f(x) and g(x))

To simplify this expression, we can use polynomial long division or synthetic division. Using synthetic division, we get:

-4 | 1 1 9

|_____-4__ 12

| 1 -3 21

Therefore, (f/g)(x) = -4x + 3 - 21 / (-4x - 3)

Simplifying further, we get:

(f/g)(x) = -4x + 3 + (21/4)(1/(x + 3/4))

Therefore, (f/g)(x) = -4x + 3 + (21/4)(1/(x + 3/4)).

Explanation:

User Sebo
by
8.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories