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What is $(f * g)(x)$ ? $\newline$ $f(x) = 2x + 6$ $\newline$ $g(x) = -2x^2$ $\newline$ 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 + 6

\newline

g(x) = -2x^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 $g(x)$ . $(f * g)(x) = f(x) * g(x)$
Define functions: We have: $\newline$ $f(x) = 2x + 6$ $\newline$ $g(x) = -2x^2$ $\newline$ Now, we need to multiply these two functions to find $(f * g)(x)$ . $\newline$ $(f * g)(x) = (2x + 6) * (-2x^2)$
Multiply functions: Distribute the terms of $f(x)$ across the terms of $g(x)$ to find the product. $(f * g)(x) = 2x * (-2x^2) + 6 * (-2x^2)$
Distribute terms: Perform the multiplication for each term. $\newline$ $(f * g)(x) = -4x^3 - 12x^2$
Perform multiplication: Express your answer as a simplified polynomial. $\newline$ The polynomial is already in its simplest form, so no further simplification is needed. $\newline$ $(f \cdot g)(x) = -4x^3 - 12x^2$

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