Question
If \( f(x)=-3 x-4, g(x)=3 x^{2}+6 x+3 \), and \( h(x)=-5 x^{2}-6 \), find \( g(1) \)
Ask by Bob Hanson. in the United States
Feb 02,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( g(1) = 12 \)
Solution
To find \( g(1) \) for the function \( g(x) = 3x^{2} + 6x + 3 \), follow these steps:
1. **Substitute \( x = 1 \) into the function:**
\[
g(1) = 3(1)^{2} + 6(1) + 3
\]
2. **Calculate each term:**
- \( 3(1)^{2} = 3 \times 1 = 3 \)
- \( 6(1) = 6 \)
- The constant term is \( 3 \)
3. **Add the results:**
\[
g(1) = 3 + 6 + 3 = 12
\]
**Therefore, \( g(1) = 12 \).**
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To find \( g(1) \), we need to substitute \( x = 1 \) into the function \( g(x) = 3x^{2} + 6x + 3 \). Calculating it step-by-step: 1. Substitute \( x = 1 \): \[ g(1) = 3(1)^{2} + 6(1) + 3 \] 2. Evaluate \( (1)^{2} \): \[ g(1) = 3(1) + 6 + 3 \] 3. Calculate \( 3(1) + 6 + 3 \): \[ g(1) = 3 + 6 + 3 = 12 \] Thus, \( g(1) = 12 \).
