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What is $(f * g)(x)$ ? $\newline$ $f(x) = 4x + 1$ $\newline$ $g(x) = 3x^2$ $\newline$ 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) = 4x + 1

\newline

g(x) = 3x^2

\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: $\newline$ $f(x) = 4x + 1$ $\newline$ $g(x) = 3x^2$ $\newline$ To find $(f * g)(x)$ , we need to multiply $f(x)$ by $g(x)$ . $\newline$ $(f * g)(x) = (4x + 1) * (3x^2)$
Distribute terms: Distribute $4x + 1$ across $3x^2$ .
$(f * g)(x) = 4x * 3x^2 + 1 * 3x^2$
Perform multiplication: Perform the multiplication. $(f \cdot g)(x) = 12x^3 + 3x^2$

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