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

\newline

g(x) = 2x^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 difference of $f(x)$ and $g(x)$ . $(f - g)(x) = f(x) - g(x)$
Find $(f - g)(x)$ : We have: $\newline$ $f(x) = 3x + 2$ $\newline$ $g(x) = 2x^2$ $\newline$ Which function represents $(f - g)(x)$ ? $\newline$ $(f - g)(x) = f(x) - g(x)$ $\newline$ $(f - g)(x) = (3x + 2) - (2x^2)$
Simplify expression: We found: $\newline$ $(f - g)(x) = (3x + 2) - (2x^2)$ $\newline$ Express your answer as a simplified polynomial or rational function. $\newline$ Distribute the negative sign through the second term. $\newline$ $(f - g)(x) = 3x + 2 - 2x^2$
Rearrange terms: Rearrange the terms in descending order of the powers of $x$ . $(f - g)(x) = -2x^2 + 3x + 2$

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