If R3 = {(x, |x| ) |x is a real number} is a relation.
Question:

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

Solution:

According to the question,

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

Domain of R3 consists of all the first elements of all the ordered pairs of R3, i.e., x,

It is also given that x is a real number,

So, Domain of R3 = R

Range of R contains all the second elements of all the ordered pairs of R3, i.e., |x|

It is also given that x is a real number,

So, |x| = |R|

⇒ |x|≥0,

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

Hence,

Range of R3 = [0, ∞)

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