To determine the values of [tex]\(g(-1.5)\)[/tex], [tex]\(g(-1.3)\)[/tex], and [tex]\(g(0.5)\)[/tex], we will use the definition of the function [tex]\(g(x)\)[/tex]. Let’s examine each case step-by-step.
1. Evaluating [tex]\(g(-1.5)\)[/tex]:
- According to the definition, for [tex]\(-2.5 < x \leq -1.5\)[/tex],
[tex]\[
g(x) = -2.
\][/tex]
- Since [tex]\(-1.5 \leq -1.5\)[/tex] holds true, it follows directly that
[tex]\[
g(-1.5) = -2.
\][/tex]
2. Evaluating [tex]\(g(-1.3)\)[/tex]:
- According to the definition, for [tex]\(-1.5 < x \leq -0.5\)[/tex],
[tex]\[
g(x) = -1.
\][/tex]
- Since [tex]\(-1.5 < -1.3 < -0.5\)[/tex] is true, it follows that
[tex]\[
g(-1.3) = -1.
\][/tex]
3. Evaluating [tex]\(g(0.5)\)[/tex]:
- According to the definition, for [tex]\(0.5 \leq x < 1.5\)[/tex],
[tex]\[
g(x) = 1.
\][/tex]
- Since [tex]\(0.5 \leq 0.5 < 1.5\)[/tex] holds true, it follows that
[tex]\[
g(0.5) = 1.
\][/tex]
Combining all the results, we have:
[tex]\[
g(-1.5) = -2,
\][/tex]
[tex]\[
g(-1.3) = -1,
\][/tex]
[tex]\[
g(0.5) = 1.
\][/tex]
Therefore, the values of [tex]\(g(-1.5)\)[/tex], [tex]\(g(-1.3)\)[/tex], and [tex]\(g(0.5)\)[/tex] are [tex]\((-2, -1, 1)\)[/tex].
