If `R_(3)={(x,|x|),|x` is a real number } is a releation, then find domain and range of `R_(3)`

Explanation

To find the domain and range of the relation \( R_3 = \{(x, |x|) \mid x \text{ is a real number}\} \), we can follow these steps:

### Step 1: Identify the Domain
The domain of a relation consists of all the first elements of the ordered pairs. In this case, the first element is \( x \), which is defined as a real number.

- Since \( x \) can take any real number value (positive, negative, or zero), the domain of \( R_3 \) is all real numbers.

**Domain:**
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