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What is $(f * g)(x)$ ? $\newline$ $f(x) = 2x^2$ $\newline$ $g(x) = x + 1$ $\newline$ 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^2

\newline

g(x) = x + 1

\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 $g(x)$ . $(f * g)(x) = f(x) * g(x)$
Define Functions: We have: $\newline$ $f(x) = 2x^2$ $\newline$ $g(x) = x + 1$ $\newline$ Now, we need to multiply these two functions to find $(f * g)(x)$ . $\newline$ $(f * g)(x) = (2x^2) * (x + 1)$
Multiply Functions: Distribute $2x^2$ to both terms in the parentheses. $\newline$ $(f * g)(x) = 2x^2 * x + 2x^2 * 1$
Distribute Terms: Perform the multiplication. $\newline$ $(f * g)(x) = 2x^3 + 2x^2$

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