Given:
The function f maps the set A = {1, 2, 3} to the set B and is defined as f = {(1, 5), (2, 6), (3, 4)}.

To find:
The set B such that the function f is invertible.

Solution:

1. Injectivity:
For a function to be invertible, it must be injective, i.e., each element in the domain A maps to a unique element in the codomain B.

Let's check if the function f is injective by examining its mapping pairs:

- f(1) = 5
- f(2) = 6
- f(3) = 4

Since each element in A maps to a unique element in B, the function f is injective.

2. Surjectivity:
For a function to be invertible, it must be surjective, i.e., every element in the codomain B has a corresponding element in the domain A.

Let's check if the function f is surjective by examining the elements in B:

- 5 is mapped from 1
- 6 is mapped from 2
- 4 is mapped from 3

Since every element in B has a corresponding element in A, the function f is surjective.

3. Invertibility:
Since the function f is both injective and surjective, it is bijective and therefore invertible.

4. Determining the Set B:
To find the set B, we need to collect all the elements that are mapped from the elements in A.

From the given mappings, we can determine that the set B = {5, 6, 4}.

Final Answer:
The set B such that the function f is invertible is B = {5, 6, 4}.

B = {4,5,6}