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What is $(f * g)(x)$ ? $\newline$ $f(x) = 3x$ $\newline$ $g(x) = 3x^2 + 4x$ $\newline$ 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

\newline

g(x) = 3x^2 + 4x

\newline

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

\newline

______

Understand Meaning: First, we need to understand what $f * g)(x)\ means. It means we need to multiply the function \$f(x)$ by the function $g(x)$ .
Write Given Functions: Now, let's write down the functions $f(x)$ and $g(x)$ that we are given: $\newline$ $f(x) = 3x$ $\newline$ $g(x) = 3x^2 + 4x$
Multiply Functions: To find $(f * g)(x)$ , we multiply $f(x)$ by $g(x)$ :
$(f * g)(x) = f(x) * g(x)$
$\phantom{=} = (3x) * (3x^2 + 4x)$
Distribute $3x$ : Distribute $3x$ across the terms in the parentheses: $\newline$ (f \cdot g)(x) = 3x \cdot 3x^2 + 3x \cdot 4x\(\newline = 9x^3 + 12x^2\)
Final Answer: The expression $9x^3 + 12x^2$ is already in simplest form, so this is our final answer.

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