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What is $(f * g)(x)$ ? $\newline$ $f(x) = 4x$ $\newline$ $g(x) = -3x + 6$ $\newline$ 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) = 4x

\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 $g(x)$ . $(f * g)(x) = f(x) * g(x)$
Given Functions: We have: $\newline$ $f(x) = 4x$ $\newline$ $g(x) = -3x + 6$ $\newline$ Which function represents $(f * g)(x)$ ? $\newline$ $(f * g)(x) = f(x) * g(x)$ $\newline$ $(f * g)(x) = 4x * (-3x + 6)$
Distribute $4x$ : We found: $\newline$ $(f * g)(x) = 4x * (-3x + 6)$ $\newline$ Now, distribute $4x$ across the terms inside the parentheses. $\newline$ $(f * g)(x) = 4x * -3x + 4x * 6$
Perform Multiplication: Perform the multiplication: f * g)(x) = \(-12x^ $2$ + $24$ x\
Simplify Polynomial: Express your answer as a simplified polynomial. $\newline$ The polynomial $-12x^2 + 24x$ is already in its simplest form.

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