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

\newline

g(x) = -2x^2 + 2x

\newline

Write your answer as a polynomial or a rational function in simplest form.

\newline

______

Identify formula: Identify the formula for $(f - g)(x)$ . $\newline$ $(f - g)(x)$ is the difference of $f(x)$ and $g(x)$ . $\newline$ $(f - g)(x) = f(x) - g(x)$
Substitute $f(x)$ and $g(x)$ : We have: $\newline$ $f(x) = -4x$ $\newline$ $g(x) = -2x^2 + 2x$ $\newline$ Substitute $f(x)$ and $g(x)$ into the formula for $(f - g)(x)$ . $\newline$ $(f - g)(x) = f(x) - g(x)$ $\newline$ $(f - g)(x) = (-4x) - (-2x^2 + 2x)$
Simplify expression: Simplify the expression by distributing the negative sign and combining like terms. $\newline$ $(f - g)(x) = -4x + 2x^2 - 2x$ $\newline$ $(f - g)(x) = 2x^2 - 4x - 2x$ $\newline$ $(f - g)(x) = 2x^2 - 6x$

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