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

\newline

g(x) = 4x

\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 $f * g$ : We have: $\newline$ $f(x) = 2x^2 - 2$ $\newline$ $g(x) = 4x$ $\newline$ To find $(f * g)(x)$ , we need to multiply $f(x)$ by $g(x)$ . $\newline$ $(f * g)(x) = (2x^2 - 2) * (4x)$
Substitute $f(x)$ and $g(x)$ : Distribute $4x$ to each term in $2x^2 - 2$ .
$(f \cdot g)(x) = 2x^2 \cdot 4x - 2 \cdot 4x$
Distribute $4x$ : Perform the multiplication. $\newline$ $(f \cdot g)(x) = 8x^3 - 8x$

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