Question
Select the correct answer. Consider functions \( f \) and \( g \). \( \begin{array}{l}f(x)=-3 x^{2}+4 x+4 \\ g(x)=x(-7 x-7) \\ \text { Which expression is equal to } f(x)+g(x) \text { ? } \\ \text { A. } \quad-3 x^{2}-3 x-3 \\ \text { B. } \quad-10 x^{2}+4 x-3 \\ \text { C. } \quad-10 x^{2}-3 x+4 \\ \text { D. } \quad 4 x^{2}-3 x+4\end{array} \) Reset Next
Ask by Rowe Harmon. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The correct expression is \( -10x^{2} - 3x + 4 \), which is option C.
Solution
To find \( f(x) + g(x) \), let's first express each function and then combine like terms.
Given:
\[
f(x) = -3x^2 + 4x + 4
\]
\[
g(x) = x(-7x - 7) = -7x^2 - 7x
\]
Now, add \( f(x) \) and \( g(x) \):
\[
f(x) + g(x) = (-3x^2 + 4x + 4) + (-7x^2 - 7x)
\]
\[
= (-3x^2 - 7x^2) + (4x - 7x) + 4
\]
\[
= -10x^2 - 3x + 4
\]
**Correct Answer:**
**C. \(-10 x^{2}-3 x+4\)**
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Simplify this solution Extra Insights
To find \( f(x) + g(x) \), we need to first calculate \( g(x) \). Given: - \( f(x) = -3x^2 + 4x + 4 \) - \( g(x) = x(-7x - 7) = -7x^2 - 7x \) Now, adding \( f(x) \) and \( g(x) \): \[ f(x) + g(x) = (-3x^2 + 4x + 4) + (-7x^2 - 7x) \] Combining like terms: \[ = -3x^2 - 7x^2 + 4x - 7x + 4 \] \[ = -10x^2 - 3x + 4 \] Thus, the expression equal to \( f(x) + g(x) \) is \( \boxed{-10x^2 - 3x + 4} \), which corresponds to option C.
