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

\newline

g(x) = -3x + 3

\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: $\newline$ $f(x) = x^2$ $\newline$ $g(x) = -3x + 3$ $\newline$ Which function represents $(f * g)(x)$ ? $\newline$ $(f * g)(x) = f(x) * g(x)$ $\newline$ $(f * g)(x) = x^2 * (-3x + 3)$
Distribute $x^2$ : Distribute $x^2$ to each term in $g(x)$ .
$(f \cdot g)(x) = x^2 \cdot (-3x) + x^2 \cdot 3$
Perform multiplication: Perform the multiplication. $\newline$ $(f \cdot g)(x) = -3x^3 + 3x^2$

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