To determine the inverse of the function [tex]\( h(x) \)[/tex], we need to swap the x and y coordinates of each pair in the set. The inverse function [tex]\( h^{-1}(x) \)[/tex] will have the original y-values as the x-values and the original x-values as the y-values. Let's go through each pair:
1. For the pair [tex]\((3, -5)\)[/tex], swapping the coordinates gives [tex]\((-5, 3)\)[/tex].
2. For the pair [tex]\((5, -7)\)[/tex], swapping the coordinates gives [tex]\((-7, 5)\)[/tex].
3. For the pair [tex]\((6, -9)\)[/tex], swapping the coordinates gives [tex]\((-9, 6)\)[/tex].
4. For the pair [tex]\((10, -12)\)[/tex], swapping the coordinates gives [tex]\((-12, 10)\)[/tex].
5. For the pair [tex]\((12, -16)\)[/tex], swapping the coordinates gives [tex]\((-16, 12)\)[/tex].
So the inverse function [tex]\( h^{-1}(x) \)[/tex] is:
[tex]\[
h^{-1}(x) = \{(-5, 3), (-7, 5), (-9, 6), (-12, 10), (-16, 12)\}
\][/tex]
Therefore, the correct answer is:
[tex]\[
\{(-5, 3), (-7, 5), (-9, 6), (-12, 10), (-16, 12)\}
\][/tex]
