To find the value of [tex]\( g(-6) \)[/tex] for the function [tex]\( g(x) = \frac{1}{3}x - 12 \)[/tex], we need to substitute [tex]\( x = -6 \)[/tex] into the function and simplify.
1. First, start with the function:
[tex]\[
g(x) = \frac{1}{3}x - 12
\][/tex]
2. Substitute [tex]\( x = -6 \)[/tex] into the function:
[tex]\[
g(-6) = \frac{1}{3}(-6) - 12
\][/tex]
3. Simplify the fraction:
[tex]\[
g(-6) = \frac{-6}{3} - 12
\][/tex]
4. Divide [tex]\( -6 \)[/tex] by [tex]\( 3 \)[/tex]:
[tex]\[
g(-6) = -2 - 12
\][/tex]
5. Finally, subtract [tex]\( 12 \)[/tex] from [tex]\( -2 \)[/tex]:
[tex]\[
g(-6) = -2 - 12 = -14
\][/tex]
Therefore, the value of [tex]\( g(-6) \)[/tex] is:
[tex]\[
g(-6) = -14
\][/tex]
