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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
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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
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