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

\newline

g(x) = -3x

\newline

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

\newline

______

Identify functions: First, we need to identify the functions $f(x)$ and $g(x)$ that we are going to multiply. $f(x) = -x + 3$ $g(x) = -3x$
Find product: Now, we will find the product $(f * g)(x)$ by multiplying $f(x)$ by $g(x)$ . $(f * g)(x) = f(x) * g(x) = (-x + 3) * (-3x)$
Distribute terms: Next, we distribute $-3x$ across the terms in the parentheses. $\newline$ $(f * g)(x) = -3x * (-x) + (-3x) * 3$
Simplify expression: We simplify the expression by performing the multiplication. $\newline$ $(f \cdot g)(x) = 3x^2 - 9x$
Check for simplest form: We check to make sure that the expression is in simplest form. Since there are no like terms to combine and no common factors to divide out, the expression is already in simplest form.

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