To find the inverse function [tex]\( h^{-1}(x) \)[/tex] from a given set of ordered pairs [tex]\( h(x) \)[/tex], we need to interchange the elements of each pair. Specifically, if [tex]\( h(x) \)[/tex] contains a pair [tex]\((a, b)\)[/tex], then [tex]\( h^{-1}(x) \)[/tex] will contain the pair [tex]\((b, a)\)[/tex].
Given the function:
[tex]\[
h(x) = \{(3, -5), (5, -7), (6, -9), (10, -12), (12, -16)\}
\][/tex]
Step-by-step interchanging the pairs:
1. For the pair [tex]\((3, -5)\)[/tex], the inverse pair is [tex]\((-5, 3)\)[/tex].
2. For the pair [tex]\((5, -7)\)[/tex], the inverse pair is [tex]\((-7, 5)\)[/tex].
3. For the pair [tex]\((6, -9)\)[/tex], the inverse pair is [tex]\((-9, 6)\)[/tex].
4. For the pair [tex]\((10, -12)\)[/tex], the inverse pair is [tex]\((-12, 10)\)[/tex].
5. For the pair [tex]\((12, -16)\)[/tex], the inverse pair is [tex]\((-16, 12)\)[/tex].
Therefore, the set of pairs for [tex]\( h^{-1}(x) \)[/tex] is:
[tex]\[
\{(-5, 3), (-7, 5), (-9, 6), (-12, 10), (-16, 12)\}
\][/tex]
Among the provided options, the set that matches our result is:
[tex]\[
\{(-5, 3), (-7, 5), (-9, 6), (-12, 10), (-16, 12)\}
\][/tex]
Thus, the correct answer is:
[tex]\[
\{(-5, 3), (-7, 5), (-9, 6), (-12, 10), (-16, 12)\}
\][/tex]
