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What is $(f * g)(x)$ ? $\newline$ $f(x) = x + 5$ $\newline$ $g(x) = 3x$ $\newline$ Write your answer as a polynomial or a rational function in simplest form. $\newline$ ______

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Power rule with rational exponents

Full solution

Q. What is

(f * g)(x)

?

\newline

f(x) = x + 5

\newline

g(x) = 3x

\newline

Write your answer as a polynomial or a rational function in simplest form.

\newline

______

Multiply Functions: To find the product $(f * g)(x)$ , we need to multiply the functions $f(x)$ and $g(x)$ together. $\newline$ $f(x) = x + 5$ $\newline$ $g(x) = 3x$ $\newline$ $(f * g)(x) = f(x) * g(x)$
Substitute Expressions: Now we substitute the expressions for $f(x)$ and $g(x)$ into the product. $(f * g)(x) = (x + 5) * (3x)$
Distribute $3x$ : Next, we distribute the $3x$ across the terms in the parentheses. $(f \cdot g)(x) = 3x \cdot x + 3x \cdot 5$
Perform Multiplication: We then perform the multiplication for each term. $\newline$ $(f * g)(x) = 3x^2 + 15x$
Final Answer: The expression $3x^2 + 15x$ is already in its simplest form, so this is our final answer. $\newline$ $(f * g)(x) = 3x^2 + 15x$

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