Find the Domain |x-1|+|x-2|=3

Problem

|x−1|+|x−2|=3

Solution

1. Identify the type of expression provided. The task asks for the domain of the equation |x−1|+|x−2|=3

2. Determine the constraints on the variable x In this equation, the absolute value functions |x−1| and |x−2| are defined for all real numbers.

3. Check for any operations that would restrict the domain, such as division by zero, square roots of negative numbers, or logarithms of non-positive numbers. None of these operations are present in the expression.

4. Conclude that since there are no restrictions on the input x the domain consists of all real numbers.

Final Answer

Domain=(−∞,∞)

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