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What is $(f * g)(x)$ ? $\newline$ $f(x) = 3x^2$ $\newline$ $g(x) = -2x + 6$ $\newline$ 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) = 3x^2

\newline

g(x) = -2x + 6

\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 $g(x)$ . $(f * g)(x) = f(x) * g(x)$
Given Functions: We have: $\newline$ $f(x) = 3x^2$ $\newline$ $g(x) = -2x + 6$ $\newline$ To find $(f * g)(x)$ , we need to multiply $f(x)$ by $g(x)$ . $\newline$ $(f * g)(x) = (3x^2) * (-2x + 6)$
Distribute Terms: Distribute $3x^2$ to both terms in the parentheses. $\newline$ $(f \cdot g)(x) = 3x^2 \cdot (-2x) + 3x^2 \cdot 6$
Perform Multiplication: Perform the multiplication. $(f \cdot g)(x) = -6x^3 + 18x^2$
Simplify Polynomial: Express your answer as a simplified polynomial. $\newline$ The polynomial $-6x^3 + 18x^2$ is already in simplest form.

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