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What is $(f * g)(x)$ ? $\newline$ $f(x) = -4x + 1$ $\newline$ $g(x) = x$ $\newline$ 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 + 1

\newline

g(x) = x

\newline

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

\newline

______

Define Product of Functions: To find the product of two functions, $f(x)$ and $g(x)$ , we multiply the two functions together. This is known as the product of functions and is denoted as $(f * g)(x)$ .
Given Functions: Given $f(x) = -4x + 1$ and $g(x) = x$ , we will multiply these two expressions to find $(f * g)(x)$ . $\newline$ $(f * g)(x) = f(x) * g(x) = (-4x + 1) * (x)$
Distribute $x$ : Now we distribute $x$ across the terms in the parentheses. $(f * g)(x) = (-4x * x) + (1 * x)$
Simplify Expression: We simplify the expression by performing the multiplication. $\newline$ $(f \cdot g)(x) = -4x^2 + x$
Final Answer: The expression $-4x^2 + x$ is already in its simplest form, so this is our final answer.

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