To determine the value of the function [tex]\( g(x) = x^3 + 6x^2 + 12x + 8 \)[/tex] when [tex]\( x = -1 \)[/tex]:
1. Substitute [tex]\( x = -1 \)[/tex] into the function:
[tex]\[
g(-1) = (-1)^3 + 6(-1)^2 + 12(-1) + 8
\][/tex]
2. Now, calculate each term step-by-step:
[tex]\[
(-1)^3 = -1
\][/tex]
[tex]\[
6(-1)^2 = 6(1) = 6
\][/tex]
[tex]\[
12(-1) = -12
\][/tex]
[tex]\[
8 \text{ (constant term)}
\][/tex]
3. Add these values together:
[tex]\[
g(-1) = -1 + 6 - 12 + 8
\][/tex]
4. Perform the addition/subtraction:
[tex]\[
g(-1) = -1 + 6 = 5
\][/tex]
[tex]\[
5 - 12 = -7
\][/tex]
[tex]\[
-7 + 8 = 1
\][/tex]
Thus, the value of the function [tex]\( g(x) \)[/tex] when [tex]\( x = -1 \)[/tex] is:
[tex]\[
g(-1) = 1
\][/tex]
So, the correct answer is:
[tex]\[
g(-1)=1
\][/tex]
