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If $R_3=\{(x,|x|) \mid x$ is a real number $\}$ is relation, then find domain and range of $R_3$.
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Given $R_3=\{(x,|x|) \mid x$ is real number $\}$
Clearly, domain $\left(R_3\right)=R$
Since, image of any real number under $R_3$ is positive real number or zero.
$\therefore \quad$ Range $\left(R_3\right)=R^{+} \cup\{0\}$ or $[0, \infty)$
Clearly, domain $\left(R_3\right)=R$
Since, image of any real number under $R_3$ is positive real number or zero.
$\therefore \quad$ Range $\left(R_3\right)=R^{+} \cup\{0\}$ or $[0, \infty)$
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