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What is $(f * g)(x)$ ? $\newline$ $f(x) = -5x + 4$ $\newline$ $g(x) = 2x$ $\newline$ 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) = -5x + 4

\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: $\newline$ $f(x) = -5x + 4$ $\newline$ $g(x) = 2x$ $\newline$ Which function represents $(f * g)(x)$ ? $\newline$ $(f * g)(x) = f(x) * g(x)$ $\newline$ $(f * g)(x) = (-5x + 4) * (2x)$
Distribute terms: Now, distribute $2x$ to each term in the polynomial $(-5x + 4)$ . $(f * g)(x) = -5x * 2x + 4 * 2x$
Perform multiplication: Perform the multiplication for each term. $\newline$ $(f \cdot g)(x) = -10x^2 + 8x$
Simplify answer: Express your answer as a simplified polynomial. $\newline$ $(f \cdot g)(x) = -10x^2 + 8x$ $\newline$ This is already in simplest form.

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