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

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Algebra 1

Power rule with rational exponents

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Q. What is

(f * g)(x)

\newline

f(x) = 3x

\newline

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

\newline

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

\newline

______

Understand $f * g)(x)\:</b> First, we need to understand what \$f * g)(x)\ means. It is the product of the functions \$f(x)$ and $g(x)$ . To find this product, we will multiply $f(x)$ by $g(x)$ .
Multiply $f(x)$ by $g(x)$ : Given $f(x) = 3x$ and $g(x) = -3x^2 + x$ , we will multiply these two expressions together. $\newline$ $(f * g)(x) = f(x) * g(x) = (3x) * (-3x^2 + x)$
Distribute $3x$ : Now, distribute $3x$ across the terms in the parentheses. $(3x) * (-3x^2 + x) = 3x * -3x^2 + 3x * x$
Perform Multiplication: Perform the multiplication for each term. $\newline$ $3x \times -3x^2 = -9x^3$ $\newline$ $3x \times x = 3x^2$
Combine Results: Combine the results to get the final expression. $\newline$ $(f * g)(x) = -9x^3 + 3x^2$

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What is (f∗g)(x)(f * g)(x)(f∗g)(x)?\newlinef(x)=3xf(x) = 3xf(x)=3x\newlineg(x)=−3x2+xg(x) = -3x^2 + xg(x)=−3x2+x\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______

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