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What is $(f * g)(x)$ ? $\newline$ $f(x) = -3x^2$ $\newline$ $g(x) = -3x + 6$ $\newline$ 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^2

\newline

g(x) = -3x + 6

\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 $g(x)$ . $(f * g)(x) = f(x) * g(x)$
Multiply Functions: We have: $\newline$ $f(x) = -3x^2$ $\newline$ $g(x) = -3x + 6$ $\newline$ Now, we need to multiply these two functions to find $(f * g)(x)$ . $\newline$ $(f * g)(x) = (-3x^2) * (-3x + 6)$
Distribute Terms: Distribute $-3x^2$ to both terms in the second function. $\newline$ $(f * g)(x) = (-3x^2) * (-3x) + (-3x^2) * 6$
Perform Multiplication: Perform the multiplication for each term. $\newline$ $(f * g)(x) = 9x^3 - 18x^2$
Combine Like Terms: Check for any like terms that can be combined. $\newline$ There are no like terms in $9x^3 - 18x^2$ , so this is the final simplified form.

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