Questions: For what value of k will the relation S=(2k+3,1),(3k-1,-2) not be a function?

Solution Steps

To determine the value of \( k \) for which the relation \( S = \{(2k+3, 1), (3k-1, -2)\} \) is not a function, we need to find when the x-values (first elements of the ordered pairs) are the same. This is because a relation is not a function if any x-value maps to more than one y-value. Therefore, we set \( 2k + 3 \) equal to \( 3k - 1 \) and solve for \( k \).

To determine the value of \( k \) for which the relation \( S = \{(2k+3, 1), (3k-1, -2)\} \) is not a function, we need to find when the x-values (first elements of the ordered pairs) are the same. This is because a relation is not a function if any x-value maps to more than one y-value. Therefore, we set \( 2k + 3 \) equal to \( 3k - 1 \).

We solve the equation \( 2k + 3 = 3k - 1 \) for \( k \).

\[ 2k + 3 = 3k - 1 \]

Subtract \( 2k \) from both sides:

\[ 3 = k - 1 \]

Add 1 to both sides:

\[ k = 4 \]

Final Answer