Question

The following function is given as a set of ordered pairs \[\left\{ {\left( {1,3} \right),\left( {3, - 2} \right),\left( {0,2} \right),\left( {5,3} \right),\left( { - 5,4} \right)} \right\}\] what is the domain of this function?

Answer 1

Hint: A set is a collection of distinct or well-defined members or elements. A set is a collection of distinct or well-defined members or elements. Ordered Pairs have x-coordinate value first followed by the corresponding y-coordinate value. Domain of the Ordered Pairs is the Set of all x-coordinate values. By using this, we will get the final output.

Complete step by step answer:
Ordered pair numbers are represented within parentheses and separated by a comma. For example, (6, 8) is an ordered-pair number whereby the numbers 6 and 8 are the first and second elements, respectively.We know that a domain is a set of all input or first values of a function. Input values are generally ‘x’ values of a function. And also, all functions are relations, but not all relations are functions.

Let: \[f:A \to B\] where f is the function of the set A and set B, then
-Set A is known as the domain of the function ‘f’.
-Set B is known as the co-domain of the function ‘f’.
Set of all f-images of all the elements of A is known as the range of ‘f’ and denoted by \[f(A)\]
Let the given ordered pairs be R, then
\[R = \left\{ {\left( {1,3} \right),\left( {3, - 2} \right),\left( {0,2} \right),\left( {5,3} \right),\left( { - 5,4} \right)} \right\}\] .
Then, we will have, \[A = \{ 1,3,0,5, - 5\} \] and \[B = \{ 3, - 2,2,3,4\} \]
Thus, the domain of the function will be:
Domain \[ = \left\{ {1,3,0,5, - 5} \right\} = A\] .

Hence, with reference to the ordered pairs given in the problem, we obtain our domain as a set of all the x-coordinate values as shown below is the domain of the function is \[\left\{ {1,3,0,5, - 5} \right\}\].

Note: A function can be defined as a rule that relates every element in one set, called the domain, to exactly one element in another set, called the range. A relation is any set of ordered-pair numbers. In other words, we can define a relation as a bunch of ordered pairs. In short, the domain of a relation from A to B is a subset of A and the range of a relation from A to B is a subset of B.