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What is $(f * g)(x)$ ? $\newline$ $f(x) = -4x$ $\newline$ $g(x) = -3x^2 - 8x$ $\newline$ Write your answer as a polynomial or a rational function in simplest form. $\newline$ ______

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Add and subtract functions

Full solution

Q. What is

(f * g)(x)

?

\newline

f(x) = -4x

\newline

g(x) = -3x^2 - 8x

\newline

Write your answer as a polynomial or a rational function in simplest form.

\newline

______

Identify Formula: Identify the formula for $(f * g)(x)$ . $(f * g)(x)$ is the product of $f(x)$ and $g(x)$ . $(f * g)(x) = f(x) * g(x)$
Given Functions: We have: $\newline$ $f(x) = -4x$ $\newline$ $g(x) = -3x^2 - 8x$ $\newline$ Now, we need to multiply these two functions to find $(f * g)(x)$ . $\newline$ $(f * g)(x) = (-4x) * (-3x^2 - 8x)$
Multiply Functions: Distribute $-4x$ across the terms in $g(x)$ :
$(f * g)(x) = (-4x) * (-3x^2) + (-4x) * (-8x)$
Distribute $-4x$ : Perform the multiplication: $\newline$ $(f \cdot g)(x) = 12x^3 + 32x^2$
Perform Multiplication: Express your answer as a simplified polynomial. $\newline$ The polynomial is already in simplest form, so we are done. $\newline$ $(f * g)(x) = 12x^3 + 32x^2$

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