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

\newline

g(x) = -x + 3

\newline

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

\newline

______

Given Functions: We are given two functions: $\newline$ f(x) = $-x$ $\newline$ g(x) = $-x + 3$ $\newline$ To find the product of these two functions, denoted as $(f * g)(x)$ , we need to multiply $f(x)$ by $g(x)$ .
Multiply Functions: Now, let's multiply the two functions: $\newline$ $(f * g)(x) = f(x) * g(x)$ $\newline$ $= (-x) * (-x + 3)$ $\newline$ We distribute the multiplication across the terms in the parentheses.
Distribute Multiplication: Performing the distribution: $\newline$ $(f * g)(x) = (-x) * (-x) + (-x) * 3$ $\newline$ $= x^2 - 3x$ $\newline$ We have multiplied each term in $g(x)$ by $-x$ .
Simplify Result: The expression $x^2 - 3x$ is already in its simplest form. It is a polynomial with no like terms to combine and no common factors to divide out.

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