Question
If \( f(x)=3 x^{2}+1 \) and \( g(x)=1-x \), what is the value of \( (f-g)(2) \) ? 12 14 36 38
Ask by Lee Lynch. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( (f - g)(2) = 14 \)
Solution
To solve for (f - g)(2), first evaluate f(2) and g(2) separately.
Step 1: Evaluate f(2)
f(x) = 3x² + 1, so
f(2) = 3*(2²) + 1 = 3*4 + 1 = 12 + 1 = 13
Step 2: Evaluate g(2)
g(x) = 1 - x, so
g(2) = 1 - 2 = -1
Step 3: Find (f - g)(2)
(f - g)(2) = f(2) - g(2) = 13 - (-1) = 13 + 1 = 14
The correct answer is 14.
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Simplify this solution Extra Insights
To find the value of \( (f-g)(2) \), we first need to calculate \( f(2) \) and \( g(2) \). 1. Calculate \( f(2) \): \[ f(2) = 3(2^2) + 1 = 3 \times 4 + 1 = 12 + 1 = 13 \] 2. Calculate \( g(2) \): \[ g(2) = 1 - 2 = -1 \] Now, we can find \( (f-g)(2) \): \[ (f-g)(2) = f(2) - g(2) = 13 - (-1) = 13 + 1 = 14 \] Thus, the value of \( (f-g)(2) \) is \( \boxed{14} \).
