# What is the domain of R: {(6, −2), (1, 2), (−3, −4), (−3, 2)} ?

Jul 9, 2015

$\setminus \emptyset$

#### Explanation:

If you're studying $\left(x , f \left(x\right)\right)$, then the domain is the first cohordinate.

dom $f = \left\{6 , 1 , - 3 , - 3\right\} \setminus R i g h t a r r o w$ indefinition at $- 3$

Elsif you're studying $\left(g \left(x\right) , x\right)$, then the domain is the second cohordinate.

dom $g = \left\{- 2 , 2 , - 4 , 2\right\} \setminus R i g h t a r r o w$ indefinition at $+ 2$

Jul 9, 2015

The domain of the relation is: {-3, 1, 6}.

#### Explanation:

The domain of a relation is the set of all numbers that occur first in an ordered pair in the relation.

For $R = \left\{\begin{matrix}6 & - 2 \\ 1 & 2 \\ - 3 & - 4 \\ - 3 & 2\end{matrix}\right\}$, the first elements are $6$, $1$, $- 3$ and $- 3$ again.

A set is completely determined by its element -- that is, by the things in the set, regardless of order of presentation of repetition, so the set:

$\left\{6 , 1 , - 3 , - 3\right\}$ is exactly the same set as the set:

{-3, 1, 6}. I've simply chosen to write the elements of the domain in increasing order.

By the way
Because the relation has two different pairs with the same first element, this relation is not a function.