Question
What is \( (f+g)(x) \) ? \[ \begin{array}{l}f(x)=-2 x^{2}-6 x \\ g(x)=-x \\ \text { Write your answer as a polynomial or a rational function in simplest form. }\end{array} \]
Ask by Little Barrett. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( (f + g)(x) = -2x^2 - 7x \)
Solution
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Extra Insights
To find \( (f+g)(x) \), we simply add the given functions \( f(x) \) and \( g(x) \): \[ f(x) + g(x) = (-2x^2 - 6x) + (-x) \] Combining the like terms: \[ = -2x^2 - 6x - x \] \[ = -2x^2 - 7x \] Thus, the simplified form of \( (f+g)(x) \) is: \[ (f+g)(x) = -2x^2 - 7x \]