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What is $(f * g)(x)$ ? $\newline$ $f(x) = x^2 - 4$ $\newline$ $g(x) = -2x$ $\newline$ 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^2 - 4

\newline

g(x) = -2x

\newline

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

\newline

______

Multiply Functions: To find the product of two functions, we multiply them together. We have $f(x) = x^2 - 4$ and $g(x) = -2x$ . Let's multiply $f(x)$ by $g(x)$ . $\newline$ Calculation: $(f * g)(x) = f(x) * g(x) = (x^2 - 4) * (-2x)$
Distribute $-2x$ : Distribute $-2x$ to each term in the polynomial $x^2 - 4$ . $\newline$ Calculation: $(f \cdot g)(x) = -2x \cdot x^2 + (-2x) \cdot (-4)$
Simplify Expression: Simplify the expression by performing the multiplication. $\newline$ Calculation: $(f \cdot g)(x) = -2x^3 + 8x$

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