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

\newline

g(x) = 3x

\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 $g(x)$ . $(f * g)(x) = f(x) * g(x)$
Determine functions: We have: $\newline$ $f(x) = 2x + 2$ $\newline$ $g(x) = 3x$ $\newline$ Which function represents $(f * g)(x)$ ? $\newline$ $(f * g)(x) = f(x) * g(x)$ $\newline$ $(f * g)(x) = (2x + 2) * (3x)$
Expand using distributive property: Expand the product using the distributive property (also known as the FOIL method for binomials): $\newline$ $(f * g)(x) = 2x * 3x + 2 * 3x$ $\newline$ $(f * g)(x) = 6x^2 + 6x$
Express as simplified polynomial: Express your answer as a simplified polynomial. $\newline$ The polynomial is already in its simplest form, so no further simplification is needed. $\newline$ $(f * g)(x) = 6x^2 + 6x$

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