If R₃ = {(x, |x| ) |x is a real number} is a relation. Then find domain and range of R₃.

Given: R₃ = {(x, |x|) |x is a real number} is a relation

To find: the domain and Range of R₃

Explanation: Given R₃ = {(x, |x|) |x is a real number}

Now we need to find the domain and range of set R₃.

So, the domain of R₃ consists of all the first elements of all the ordered pairs of R₃, i.e., x, and it is also given x is a real number, so

Domain of R₃ = R

And the range of R contains all the second elements of all the ordered pairs of R₃, 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 R₃ = [0, ∞)