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

\newline

g(x) = -2x + 5

\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: $\newline$ $f(x) = -x$ $\newline$ $g(x) = -2x + 5$ $\newline$ Which function represents $(f * g)(x)$ ? $\newline$ $(f * g)(x) = f(x) * g(x)$ $\newline$ $(f * g)(x) = (-x) * (-2x + 5)$
Distribute $-x$ : Now, distribute $-x$ across the terms in $g(x)$ :
$(f \cdot g)(x) = (-x) \cdot (-2x) + (-x) \cdot 5$
Perform Multiplication: Perform the multiplication: $\newline$ $(f \cdot g)(x) = 2x^2 - 5x$
Express Answer: Express your answer as a simplified polynomial. $\newline$ The polynomial $2x^2 - 5x$ is already in its simplest form.

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