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

\newline

g(x) = 2x^2 - 5x

\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: $\newline$ $f(x) = 2x$ $\newline$ $g(x) = 2x^2 - 5x$ $\newline$ Now, we need to multiply these two functions to find $(f * g)(x)$ . $\newline$ $(f * g)(x) = (2x) * (2x^2 - 5x)$
Multiply functions: Distribute $2x$ across the terms in $g(x)$ .
$(f * g)(x) = 2x * 2x^2 - 2x * 5x$
Distribute $2x$ : Perform the multiplication for each term. $(f \cdot g)(x) = 4x^3 - 10x^2$
Perform multiplication: Check for any like terms that can be combined. $\newline$ There are no like terms in $4x^3 - 10x^2$ , so this is the final simplified form.

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