Question
\( g(n)=-4 n+5 \) \( h(n)=n^{3}+2-n \) Find \( (g+h)(n) \)
Ask by Clark Watkins. in the United States
Feb 04,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\((g + h)(n) = n^3 - 5n + 7\)
Solution
To find \((g + h)(n)\), you simply add the corresponding expressions of \(g(n)\) and \(h(n)\):
\[
\begin{align*}
g(n) &= -4n + 5 \\
h(n) &= n^3 + 2 - n \\
(g + h)(n) &= g(n) + h(n) \\
&= (-4n + 5) + (n^3 + 2 - n) \\
&= n^3 - 4n - n + 5 + 2 \\
&= n^3 - 5n + 7
\end{align*}
\]
**Final Answer:**
\[
(g + h)(n) = n^3 - 5n + 7
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To find \( (g+h)(n) \), we simply add the two functions \( g(n) \) and \( h(n) \). Starting with \( g(n) = -4n + 5 \) and \( h(n) = n^3 + 2 - n \), we perform the addition: \[ (g+h)(n) = g(n) + h(n) = (-4n + 5) + (n^3 + 2 - n) \] Now, combine like terms: \[ (g+h)(n) = n^3 + (-4n - n) + (5 + 2) \] This simplifies to: \[ (g+h)(n) = n^3 - 5n + 7 \] So, the result is: \[ (g+h)(n) = n^3 - 5n + 7 \]
