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

\newline

g(x) = -3x + 3

\newline

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

\newline

______

Identify formula for $(f * g)(x)$ : Identify the formula for $(f * g)(x)$ . $(f * g)(x)$ is the product of $f(x)$ and $g(x)$ . $(f * g)(x) = f(x) * g(x)$
Multiply $f(x)$ and $g(x)$ : We have: $\newline$ $f(x) = -x^2$ $\newline$ $g(x) = -3x + 3$ $\newline$ Now, we need to multiply these two functions to find $(f * g)(x)$ . $\newline$ $(f * g)(x) = (-x^2) * (-3x + 3)$
Distribute $-x^2$ : Distribute $-x^2$ to both terms in the parentheses. $\newline$ $(f \cdot g)(x) = (-x^2) \cdot (-3x) + (-x^2) \cdot 3$
Perform multiplication for each term: Perform the multiplication for each term. $(f * g)(x) = 3x^3 - 3x^2$
Express answer as simplified polynomial: Express your answer as a simplified polynomial. $\newline$ The polynomial is already in its simplest form, so no further simplification is needed. $\newline$ $(f * g)(x) = 3x^3 - 3x^2$

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