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What is $(f * g)(x)$ ? $\newline$ $f(x) = 4x + 4$ $\newline$ $g(x) = -x$ $\newline$ Write your answer as a polynomial or a rational function in simplest form. $\newline$ ______

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Power rule with rational exponents

Full solution

Q. What is

(f * g)(x)

?

\newline

f(x) = 4x + 4

\newline

g(x) = -x

\newline

Write your answer as a polynomial or a rational function in simplest form.

\newline

______

Multiply $f$ by $g$ : We have $f(x) = 4x + 4$ and $g(x) = -x$ . To find $(f * g)(x)$ , we multiply $f(x)$ by $g(x)$ : $(f * g)(x) = f(x) * g(x) = (4x + 4) * (-x)$ .
Distribute $-x$ : Now we distribute $-x$ to each term in the parentheses: $\newline$ $(f \cdot g)(x) = -x \cdot 4x + (-x) \cdot 4$ .
Simplify the expression: Simplify the expression by performing the multiplication: f \cdot g)(x) = \(-4x^ $2$ - $4$ x.
Simplify the expression: Simplify the expression by performing the multiplication: $\newline$ $(f * g)(x) = -4x^2 - 4x$ .The expression $-4x^2 - 4x$ is already in simplest form, as there are no like terms to combine and no further simplification possible.

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