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

\newline

g(x) = -2x

\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: $\newline$ $f(x) = 2x + 3$ $\newline$ $g(x) = -2x$ $\newline$ Which function represents $(f * g)(x)$ ? $\newline$ $(f * g)(x) = f(x) * g(x)$ $\newline$ $(f * g)(x) = (2x + 3) * (-2x)$
Distribute $-2x$ : We found: $\newline$ $(f * g)(x) = (2x + 3) * (-2x)$ $\newline$ Now, distribute $-2x$ to both terms in the parentheses. $\newline$ $(f * g)(x) = 2x * (-2x) + 3 * (-2x)$
Perform multiplication: Perform the multiplication. $(f \cdot g)(x) = -4x^2 - 6x$

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