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What is $(f + g)(x)$ ? $\newline$ $f(x) = -x^2 - 3x$ $\newline$ $g(x) = x^2$ $\newline$ Write your answer as a polynomial or a rational function in simplest form.

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Add and subtract functions

Full solution

Q. What is

(f + g)(x)

?

\newline

f(x) = -x^2 - 3x

\newline

g(x) = x^2

\newline

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

Combine Functions: $(f + g)(x) = f(x) + g(x)$ $\newline$ We have $f(x) = -x^2 - 3x$ and $g(x) = x^2$ . Let's add these two functions. $\newline$ $(f + g)(x) = (-x^2 - 3x) + (x^2)$
Add Functions: Now, we combine like terms. The $-x^2$ from $f(x)$ and the $x^2$ from $g(x)$ cancel each other out. $\newline$ $(f + g)(x) = -x^2 + x^2 - 3x$ $\newline$ $(f + g)(x) = -3x$

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