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What is $(f * g)(x)$ ? $\newline$ $f(x) = -3x + 5$ $\newline$ $g(x) = 2x$ $\newline$ 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) = -3x + 5

\newline

g(x) = 2x

\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: $\newline$ $f(x) = -3x + 5$ $\newline$ $g(x) = 2x$ $\newline$ To find $(f * g)(x)$ , we need to multiply $f(x)$ by $g(x)$ . $\newline$ $(f * g)(x) = (-3x + 5) * (2x)$
Distribute Terms: Distribute $2x$ to each term in the first polynomial. $\newline$ $(f * g)(x) = -3x * 2x + 5 * 2x$
Perform Multiplication: Perform the multiplication for each term. $\newline$ $(f \cdot g)(x) = -6x^2 + 10x$
Final Answer: The expression $-6x^2 + 10x$ is already in its simplest form, so this is our final answer.

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