If R3 = {(x, |x| ) |x is a real number} is a relation. Then find doma

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

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

Answer»

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, ∞)