To solve the problem, we need to find the value of the function [tex]\( g(N) = 3N^2 - 2N - 6 \)[/tex] at [tex]\( N = -2 \)[/tex].
Let's substitute [tex]\( N = -2 \)[/tex] into the function:
[tex]\[
g(-2) = 3(-2)^2 - 2(-2) - 6
\][/tex]
First, we need to calculate each term separately:
1. Calculate [tex]\( (-2)^2 \)[/tex]:
[tex]\[
(-2)^2 = 4
\][/tex]
2. Multiply this result by 3:
[tex]\[
3 \times 4 = 12
\][/tex]
3. Calculate [tex]\( -2 \times (-2) \)[/tex]:
[tex]\[
-2 \times (-2) = 4
\][/tex]
4. Now, sum these results and subtract 6:
[tex]\[
g(-2) = 12 + 4 - 6
\][/tex]
5. Finally, perform the addition and subtraction:
[tex]\[
12 + 4 = 16
\][/tex]
[tex]\[
16 - 6 = 10
\][/tex]
Thus, the value of [tex]\( g(-2) \)[/tex] is 10. Therefore, the correct answer is:
C) 10
