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

\newline

g(x) = x

\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 $g(x)$ . $(f * g)(x) = f(x) * g(x)$
Find product: We have: $\newline$ $f(x) = 2x^2 - 6x$ $\newline$ $g(x) = x$ $\newline$ To find $(f * g)(x)$ , we multiply $f(x)$ by $g(x)$ . $\newline$ $(f * g)(x) = (2x^2 - 6x) * x$
Perform multiplication: Perform the multiplication: $\newline$ $(f * g)(x) = 2x^2 * x - 6x * x$ $\newline$ $(f * g)(x) = 2x^3 - 6x^2$
Express answer: Express your answer as a simplified polynomial. $\newline$ The polynomial is already in its simplest form, so no further simplification is needed. $\newline$ $(f * g)(x) = 2x^3 - 6x^2$

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