Answer :

Given: R_{3} = {(x, |x|) |x is a real number} is a relation

To find: the domain and Range of R_{3}

Explanation: Given R_{3} = {(x, |x|) |x is a real number}

Now we need to find the domain and range of set R_{3}.

So, the domain of R_{3} consists of all the first elements of all the ordered pairs of R_{3}, i.e., x, and it is also given x is a real number, so

Domain of R_{3} = R

And the range of R contains all the second elements of all the ordered pairs of R_{3}, i.e., |x| and it is also given x is a real number, so

|x| = |R|

⇒ |x|≥0,

i.e., |x| has all positive real numbers including 0

So,

Range of R_{3} = [0, ∞)

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