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The function [tex]\( h(x) \)[/tex] is given below:
[tex]\[ h(x) = \{(3, -5), (5, -7), (6, -9), (10, -12), (12, -16)\} \][/tex]

Which of the following gives [tex]\( h^{-1}(x) \)[/tex]?

A. [tex]\(\{(3, 5), (5, 7), (6, 9), (10, 12), (12, 16)\}\)[/tex]

B. [tex]\(\{(-5, 3), (-7, 5), (-9, 6), (-12, 10), (-16, 12)\}\)[/tex]

C. [tex]\(\{(3, -5), (5, -7), (6, -9), (10, -12), (12, -16)\}\)[/tex]

D. [tex]\(\{(5, 3), (7, 5), (9, 6), (12, 10), (16, 12)\}\)[/tex]



Answer :

GinnyAnswer
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]

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