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

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Power rule with rational exponents

Full solution

Q. What is

(f * g)(x)

?

\newline

f(x) = 3x + 3

\newline

g(x) = -3x^2

\newline

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

\newline

______

Identify functions: First, we need to identify the functions $f(x)$ and $g(x)$ that we will be multiplying together. $\newline$ $f(x) = 3x + 3$ $\newline$ $g(x) = -3x^2$
Multiply functions: Next, we will multiply $f(x)$ by $g(x)$ to find the product $(f * g)(x)$ . This is done by multiplying each term in $f(x)$ by each term in $g(x)$ . $(3x + 3)(-3x^2) = 3x * (-3x^2) + 3 * (-3x^2)$
Perform multiplication: Now, we perform the multiplication for each term. $\newline$ $3x \times (-3x^2) = -9x^3$ $\newline$ $3 \times (-3x^2) = -9x^2$
Combine results: Combine the results of the multiplication to get the final polynomial. $\newline$ $(f * g)(x) = -9x^3 - 9x^2$

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