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

\newline

g(x) = 2x + 5

\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 $g(x)$ . $(f - g)(x) = f(x) - g(x)$
Substitute Functions: We have: $\newline$ $f(x) = -3x$ $\newline$ $g(x) = 2x + 5$ $\newline$ Substitute the functions into the formula for $(f - g)(x)$ . $\newline$ $(f - g)(x) = f(x) - g(x)$ $\newline$ $(f - g)(x) = (-3x) - (2x + 5)$
Simplify Expression: Simplify the expression by distributing the negative sign and combining like terms. $\newline$ $(f - g)(x) = -3x - 2x - 5$ $\newline$ Combine the like terms $-3x$ and $-2x$ . $\newline$ $(f - g)(x) = -5x - 5$

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