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What is $(f * g)(x)$ ? $\newline$ $f(x) = 5x + 3$ $\newline$ $g(x) = -4x$ $\newline$ 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) = 5x + 3

\newline

g(x) = -4x

\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: $\newline$ $f(x) = 5x + 3$ $\newline$ $g(x) = -4x$ $\newline$ Which function represents $(f * g)(x)$ ? $\newline$ $(f * g)(x) = f(x) * g(x)$ $\newline$ $(f * g)(x) = (5x + 3) * (-4x)$
Distribute Terms: Now, distribute $-4x$ to both terms in the parentheses: $\newline$ $(f \cdot g)(x) = 5x \cdot (-4x) + 3 \cdot (-4x)$ $\newline$ $(f \cdot g)(x) = -20x^2 - 12x$
Simplified Expression: Express your answer as a simplified polynomial or rational function. $\newline$ The expression is already simplified: $\newline$ $(f \cdot g)(x) = -20x^2 - 12x$

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