Question: Find a value of \( k \) such that the relation \( \{ (k, 4), (9, 5), (2, 1), (6, 8) \} \)…

Find a value of \( k \) such that the relation \( \{ (k, 4), (9, 5), (2, 1), (6, 8) \} \) does not have a domain of \( \{2, 6, 9\} \).

\( k = \) Enter your next step here

Solution

The problem is asking you to find a value of \( k \) such that the relation \[ \{ (k, 4), (9, 5), (2, 1), (6, 8) \} \] does not map more than one input to different outputs, making sure it is a function. A relation is a function if each input is associated with exactly one output. This means that no two pairs should have the same first element (input) and different second elements (outputs). Check the existing inputs in the given relation: - \( k \) - \( 9 \) - \( 2 \) - \( 6 \) Ensure \( k \) is not equal to any of these existing inputs to maintain the functionality. Therefore, \( k \) should not be \( 9, 2, \) or \( 6 \). Since these numbers make the relation non-functional if chosen, any number other than these will ensure that the relation remains a function. Hence, \( k \) should be any value other than \( 9, 2, \) or \( 6 \).