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

\newline

g(x) = -4x

\newline

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

\newline

______

Multiply Functions: To find the product of two functions, we multiply them together. We have $f(x) = 3x^2 - 3$ and $g(x) = -4x$ . Let's multiply $f(x)$ by $g(x)$ .
Distribute $-4x$ : $(f \cdot g)(x) = f(x) \cdot g(x) = (3x^2 - 3) \cdot (-4x)$ We distribute $-4x$ to each term in the parentheses.
Perform Multiplication: $(f * g)(x) = 3x^2 * (-4x) + (-3) * (-4x)$ $\newline$ Now we perform the multiplication for each term.
Simplify Expression: $(f \cdot g)(x) = -12x^3 + 12x$ $\newline$ We have multiplied each term correctly and simplified the expression.
Final Answer: The final answer is a polynomial in simplest form.

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