Let's determine the values of the function [tex]\( g \)[/tex] at specific points.
1. For [tex]\( x = -2 \)[/tex]:
- We need to check which interval [tex]\(-2\)[/tex] falls into.
- Looking at the intervals, [tex]\(-2\)[/tex] is within [tex]\([-2, 4)\)[/tex].
- In this interval, the function [tex]\( g(x) \)[/tex] is defined as [tex]\( 0 \)[/tex].
Therefore,
[tex]\[
g(-2) = 0
\][/tex]
2. For [tex]\( x = 4 \)[/tex]:
- We need to check which interval [tex]\(4\)[/tex] falls into.
- Looking at the intervals, [tex]\(4\)[/tex] is within [tex]\([4, 10)\)[/tex].
- In this interval, the function [tex]\( g(x) \)[/tex] is defined as [tex]\( -4 \)[/tex].
Therefore,
[tex]\[
g(4) = -4
\][/tex]
So, the values of the function are:
[tex]\[
g(-2) = 0
\][/tex]
[tex]\[
g(4) = -4
\][/tex]