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What is $(f * g)(x)$ ? $\newline$ $f(x) = 3x + 1$ $\newline$ $g(x) = -x^2$ $\newline$ 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) = 3x + 1

\newline

g(x) = -x^2

\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 $g(x)$ . $(f * g)(x) = f(x) * g(x)$
Calculate Product: We have: $\newline$ $f(x) = 3x + 1$ $\newline$ $g(x) = -x^2$ $\newline$ Now, calculate the product $(f * g)(x)$ by multiplying $f(x)$ and $g(x)$ together. $\newline$ $(f * g)(x) = (3x + 1) * (-x^2)$
Distribute Terms: Distribute $-x^2$ to each term in the binomial $(3x + 1)$ . $\newline$ $(f * g)(x) = 3x * (-x^2) + 1 * (-x^2)$
Perform Multiplication: Perform the multiplication for each term. $\newline$ $(f * g)(x) = -3x^3 - x^2$
Express Answer: Express your answer as a simplified polynomial. The polynomial is already in its simplest form, so no further simplification is needed.

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