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

\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 $g(x)$ . $(f * g)(x) = f(x) * g(x)$
Given Functions: We have: $\newline$ $f(x) = 2x + 4$ $\newline$ $g(x) = x$ $\newline$ Which function represents $(f * g)(x)$ ? $\newline$ $(f * g)(x) = f(x) * g(x)$ $\newline$ $(f * g)(x) = (2x + 4) * x$
Calculate Product: We found: $\newline$ $(f * g)(x) = (2x + 4) * x$ $\newline$ Now, distribute $x$ to both terms in the parentheses. $\newline$ $(f * g)(x) = 2x * x + 4 * x$
Distribute $x$ : Simplify the expression by performing the multiplication. $(f \cdot g)(x) = 2x^2 + 4x$ Express your answer as a simplified polynomial.

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