Determine whether the function f defined by the set of ordered pairs has an inverse. If it​ does, find the inverse.

Question

StartSet left parenthesis 6 comma 2 right parenthesis comma left parenthesis 3 comma 1 right parenthesis comma left parenthesis 1 comma 6 right parenthesis comma left parenthesis 4 comma 2 right parenthesis EndSet
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Part 1
Select the correct choice below​ and, if​ necessary, fill in any answer boxes within your choice.
A.
The inverse function is StartSet nothing EndSet
  
.
​(Type ordered pairs. Use a comma to separate answers as​ needed.)
B.
The function does not have an inverse.

Answer 1

To determine whether the function has an inverse, we need to check if the function is one-to-one (injective). A function is one-to-one if no two different ordered pairs have the same second element.

We can list the pairs from the function:

1. (6, 2)
2. (3, 1)
3. (1, 6)
4. (4, 2)

Next, we look at the second elements of each ordered pair:

• The second elements are: 2 (from (6,2)), 1 (from (3,1)), 6 (from (1,6)), and 2 (from (4,2)).

We can see that the second element "2" is repeated in the pairs (6, 2) and (4, 2). This means that the function is not one-to-one.

Since the function is not one-to-one, it does not have an inverse.

So the correct choice is: B. The function does not have an inverse.