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What is $(f * g)(x)$ ? $\newline$ $f(x) = 2x$ $\newline$ $g(x) = 4x + 1$ $\newline$ 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

\newline

g(x) = 4x + 1

\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 $g(x)$ . $(f * g)(x) = f(x) * g(x)$
Calculate product: We have: $\newline$ $f(x) = 2x$ $\newline$ $g(x) = 4x + 1$ $\newline$ Now, calculate the product of $f(x)$ and $g(x)$ to find $(f * g)(x)$ . $\newline$ $(f * g)(x) = (2x) * (4x + 1)$
Distribute $2x$ : Distribute $2x$ across the terms in the parentheses. $\newline$ $(f \cdot g)(x) = 2x \cdot 4x + 2x \cdot 1$
Perform multiplication: Perform the multiplication. $\newline$ $(f \cdot g)(x) = 8x^2 + 2x$
Express as polynomial: Express your answer as a simplified polynomial. $\newline$ The polynomial $8x^2 + 2x$ is already in its simplest form.

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