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Identify the inverse [tex]\( g(x) \)[/tex] of the given relation [tex]\( f(x) \)[/tex].

[tex]\( f(x) = \{(8, 3), (4, 1), (0, -1), (-4, -3)\} \)[/tex]

A. [tex]\( g(x) = \{(-4, -3), (0, -1), (4, 1), (8, 3)\} \)[/tex]

B. [tex]\( g(x) = \{(-8, -3), (-4, 1), (0, 1), (4, 3)\} \)[/tex]

C. [tex]\( g(x) = \{(8, -3), (4, -1), (0, 1), (-4, 3)\} \)[/tex]

D. [tex]\( g(x) = \{(3, 8), (1, 4), (-1, 0), (-3, -4)\} \)[/tex]



Answer :

GinnyAnswer
To identify the inverse [tex]\( g(x) \)[/tex] of the given relation [tex]\( f(x) \)[/tex], we need to understand what it means to find the inverse of a relation. The inverse of a relation swaps the roles of the inputs (domain) and outputs (range).

Given:
[tex]\[ f(x) = \{(8, 3), (4, 1), (0, -1), (-4, -3)\} \][/tex]

To find [tex]\( g(x) \)[/tex], the inverse of [tex]\( f(x) \)[/tex], we swap each pair’s elements. Here are the detailed steps:

1. Take the pair [tex]\((8, 3)\)[/tex]:
- Swap the elements to get [tex]\((3, 8)\)[/tex].

2. Take the pair [tex]\((4, 1)\)[/tex]:
- Swap the elements to get [tex]\((1, 4)\)[/tex].

3. Take the pair [tex]\((0, -1)\)[/tex]:
- Swap the elements to get [tex]\((-1, 0)\)[/tex].

4. Take the pair [tex]\((-4, -3)\)[/tex]:
- Swap the elements to get [tex]\((-3, -4)\)[/tex].

Thus, the inverse relation [tex]\( g(x) \)[/tex] is:
[tex]\[ g(x) = \{(3, 8), (1, 4), (-1, 0), (-3, -4)\} \][/tex]

So, the correct answer is:
[tex]\[ g(x) = \{(3, 8), (1, 4), (-1, 0), (-3, -4)\} \][/tex]

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