If $R_3$ = {(x, |x| ) |x is a real number} is a relation. Then find domain and range of $R_3$.

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If $R_3$ = {(x, |x| ) |x is a real number} is a relation. Then find domain and range of $R_3$ .

If $R_3$ = {(x, |x| ) |x is a real number} is a relation. Then find domain and range of $R_3$ .

Solution:

Provided,

$\mathrm{R}_3=\{(\mathrm{x},|\mathrm{x}|) \mid \mathrm{x}$ is a real number $\}$ is a relation

All the first elements of all the ordered pairs of R3, i.e., x, are included in thec domain of $R_3$

Also provided that x is a real number,

Therefore, Domain of $R_3 = R$

All the second elements of all the ordered pairs of R3, i.e., |x| are included in the range of R.

Also provided that x is a real number,

Therefore, $|x|=|R|$

$\Rightarrow \quad|x| \geq 0$

Therefore, |x| has all positive real numbers including 0

As a result,

Range of $\mathrm{R}_3=[0, \infty)$

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