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What is $(f * g)(x)$ ? $\newline$ $f(x) = -2x$ $\newline$ $g(x) = -2x^2 + 2$ $\newline$ Write your answer as a polynomial or a rational function in simplest form. $\newline$ ______

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Add and subtract functions

Full solution

Q. What is

(f * g)(x)

?

\newline

f(x) = -2x

\newline

g(x) = -2x^2 + 2

\newline

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

\newline

______

Identify Formula: Identify the formula for $(f * g)(x)$ . $(f * g)(x)$ is the product of $f(x)$ and $g(x)$ . $(f * g)(x) = f(x) * g(x)$
Multiply Functions: We have: $\newline$ $f(x) = -2x$ $\newline$ $g(x) = -2x^2 + 2$ $\newline$ Now, we need to multiply these two functions to find $(f * g)(x)$ . $\newline$ $(f * g)(x) = (-2x) * (-2x^2 + 2)$
Distribute $-2x$ : Distribute $-2x$ across the terms in $g(x)$ . $(f * g)(x) = (-2x) * (-2x^2) + (-2x) * 2$
Perform Multiplication: Perform the multiplication. $(f \cdot g)(x) = 4x^3 - 4x$
Express Answer: Express your answer as a simplified polynomial. $\newline$ The polynomial is already in its simplest form, so we are done. $\newline$ $(f * g)(x) = 4x^3 - 4x$

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