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What is $(f * g)(x)$ ? $\newline$ $f(x) = -5x + 3$ $\newline$ $g(x) = 3x^2$ $\newline$ 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) = -5x + 3

\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 $g(x)$ . $(f * g)(x) = f(x) * g(x)$
Given functions: We have: $\newline$ $f(x) = -5x + 3$ $\newline$ $g(x) = 3x^2$ $\newline$ Now, we need to multiply these two functions to find $(f * g)(x)$ . $\newline$ $(f * g)(x) = (-5x + 3) * (3x^2)$
Multiply functions: Distribute each term in the first polynomial over the second polynomial. $\newline$ $(-5x + 3) \times (3x^2) = (-5x \times 3x^2) + (3 \times 3x^2)$
Distribute terms: Perform the multiplication for each term. $\newline$ $(-5x \times 3x^2) = -15x^3$ $\newline$ $(3 \times 3x^2) = 9x^2$ $\newline$ So, $(f \times g)(x) = -15x^3 + 9x^2$

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