Question
\( g(n)=n^{2}+4+2 n \) \( h(n)=-3 n+2 \) Find \( (g \cdot h)(1) \)
Ask by Murphy Coleman. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\((g \cdot h)(1) = -7\)
Solution
To find \((g \cdot h)(1)\), we first need to understand that \((g \cdot h)(n)\) represents the product of the functions \(g(n)\) and \(h(n)\). Therefore:
\[
(g \cdot h)(n) = g(n) \times h(n)
\]
Given the functions:
\[
g(n) = n^2 + 2n + 4
\]
\[
h(n) = -3n + 2
\]
Let's evaluate each function at \(n = 1\):
1. **Calculate \(g(1)\):**
\[
g(1) = (1)^2 + 2(1) + 4 = 1 + 2 + 4 = 7
\]
2. **Calculate \(h(1)\):**
\[
h(1) = -3(1) + 2 = -3 + 2 = -1
\]
3. **Multiply the results:**
\[
(g \cdot h)(1) = g(1) \times h(1) = 7 \times (-1) = -7
\]
**Final Answer:** \(-7\)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To find \( (g \cdot h)(1) \), we first need to calculate \( g(1) \) and \( h(1) \). Starting with \( g(n) = n^2 + 2n + 4 \): \[ g(1) = 1^2 + 2(1) + 4 = 1 + 2 + 4 = 7 \] Next, for \( h(n) = -3n + 2 \): \[ h(1) = -3(1) + 2 = -3 + 2 = -1 \] Now we find \( (g \cdot h)(1) \): \[ (g \cdot h)(1) = g(1) \cdot h(1) = 7 \cdot (-1) = -7 \] Thus, \( (g \cdot h)(1) = -7 \).
