To determine the function's value when [tex]\( x = -1 \)[/tex], we need to evaluate [tex]\( g(-1) \)[/tex] for the given function [tex]\( g(x) = x^3 + 6x^2 + 12x + 8 \)[/tex].
Let's calculate [tex]\( g(-1) \)[/tex] step-by-step:
1. Substitute [tex]\( x = -1 \)[/tex] into the function:
[tex]\( g(-1) = (-1)^3 + 6(-1)^2 + 12(-1) + 8 \)[/tex]
2. Evaluate each term individually:
[tex]\[ (-1)^3 = -1 \][/tex]
[tex]\[ 6(-1)^2 = 6 \times 1 = 6 \][/tex]
[tex]\[ 12(-1) = -12 \][/tex]
[tex]\[ 8 = 8 \][/tex]
3. Combine all the evaluated terms:
[tex]\[ g(-1) = -1 + 6 - 12 + 8 \][/tex]
4. Perform the arithmetic operations:
[tex]\[ g(-1) = -1 + 6 = 5 \][/tex]
[tex]\[ 5 - 12 = -7 \][/tex]
[tex]\[ -7 + 8 = 1 \][/tex]
Therefore, the value of [tex]\( g(-1) \)[/tex] is [tex]\( 1 \)[/tex]. The correct answer is [tex]\( g(-1) = 1 \)[/tex].
[tex]\[
\boxed{g(-1)=1}
\][/tex]
