Question

Determine if the function f defined by the arrow diagram to the right has an inverse. If it​ does, create an arrow diagram that defines the inverse. If​ not, explain why not.
2
4
0
7
5
8
0
4
Domain
Range
f
Question content area bottom
Part 1
Choose the correct answer below.
A.
5
8
0
4
2
4
0
7
f Superscript negative 1
Domain
Range
B.
5
8
0
4
7
0
4
2
f Superscript negative 1
Domain
Range
C.
7
0
4
2
5
8
0
4
f Superscript negative 1
Domain
Range
D.
This function does not have an inverse because it is not​ one-to-one.

Answer 1

To determine if the function \( f \) represented by the arrow diagram has an inverse, we need to check if the function is one-to-one. A function is one-to-one if it assigns a unique output for every unique input, meaning no two different inputs map to the same output.

Let's analyze the mapping given the elements:

- If the function maps several elements from the domain to the same element in the range, then it is not one-to-one.

Now let's examine the mappings you presented:

- We have potential inputs (Domain): 2, 4, 0, 7, 5
- And potential outputs (Range): 8, 0, 4

If any of the inputs (2, 4, 0, 7, 5) maps to the same output in the range, it means multiple inputs result in the same output, indicating the function is not one-to-one.

Without the specific mappings from the diagram itself (as I can't see it), I can deduce the general answer:

If any two inputs share the same output, the function is not one-to-one.

Given these conditions, here are the possible answers based on your options:

If the function is not one-to-one:
**D. This function does not have an inverse because it is not​ one-to-one.**

If the function is one-to-one:
You would create an arrow diagram that reverses the mappings (output to input). However, without seeing the original mappings, I cannot provide a specific inverse.

Hence, if you've determined it is not one-to-one based on the mappings, the answer is D. If not, you may need to find the specific pair mappings to verify.