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What is $(f * g)(x)$ ? $\newline$ $f(x) = 3x + 6$ $\newline$ $g(x) = -5x$ $\newline$ 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 + 6

\newline

g(x) = -5x

\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 $g(x)$ . $(f * g)(x) = f(x) * g(x)$
Given functions: We have: $\newline$ $f(x) = 3x + 6$ $\newline$ $g(x) = -5x$ $\newline$ Now, we need to multiply these two functions to find $(f * g)(x)$ . $\newline$ $(f * g)(x) = (3x + 6) * (-5x)$
Distribute terms: Distribute $-5x$ to both terms in the parentheses. $\newline$ $(f \cdot g)(x) = 3x \cdot (-5x) + 6 \cdot (-5x)$
Perform multiplication: Perform the multiplication. $(f \cdot g)(x) = -15x^2 - 30x$
Final answer: Express your answer as a simplified polynomial. $\newline$ The expression $-15x^2 - 30x$ is already in its simplest form, so this is our final answer.

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