Question

question 13
find the domain of the function $f(x) = \frac{1}{6x + 7}$. what is the only value
only value=
question 14
think about the following relation: \\{(7,-3),(5,0),(7,4),(-1,0)\\}
what is the domain of the relation? \\{ \\}

Explanation:

Question 13

Step1: Identify the restriction

For the function \( f(x)=\frac{1}{6x + 7} \), the denominator cannot be zero. So we set \( 6x+7=0 \) to find the value that \( x \) cannot take.

Step2: Solve for \( x \)

Subtract 7 from both sides: \( 6x=-7 \)
Divide both sides by 6: \( x = -\frac{7}{6} \)

The domain of a relation (set of ordered pairs) is the set of all first elements (x - values) of the ordered pairs. Given the relation \( \{(7, - 3),(5,0),(7,4),(-1,0)\} \), we list the unique first elements.
The first elements are 7, 5, 7, - 1. After removing duplicates, the domain elements are - 1, 5, 7.

Answer:

\( -\frac{7}{6} \)

Question 14