Question

Let f be defined as shown. If the domain is

restricted to {3,5}, which statement is true?
Answers
The Inverse if F exists
The inverse of f does not exist

Answer 1

To determine if the inverse of a function
`\( f \)` exists, the function must be one-to-one (injective), meaning that each element in the domain is mapped to a unique element in the codomain. In other words, no two different elements in the domain can map to the same element in the codomain.

If the domain of
`\( f \)` is restricted to {1,5}, we need to look at where 1 and 5 map to in the output. For an inverse function to exist, 1 and 5 must both map to different numbers in the output.

From the image provided, we can't see the mappings, but to answer this question, you would proceed as follows:

1. Check the mappings of 1 and 5 in the diagram.

2. If 1 and 5 map to two different numbers in the output, then the inverse of
`\( f \)` exists.

3. If 1 and 5 map to the same number, or if there is any ambiguity in the mapping (such as 1 or 5 mapping to multiple numbers), then the inverse of
`\( f \)` does not exist.

Answer 2

Inverse of F does not exist

Explanation:

2 different x values lead to 1 y value therefore it cannot be reversed