Find the Domain

Problem

√(,4*x−3)−√(,2*x−5)=2

Solution

1. Identify the constraints for the square root functions, as the radicand (the expression inside the square root) must be greater than or equal to zero for the result to be a real number.

2. Set up the first inequality for the term √(,4*x−3)

4*x−3≥0

3. Solve the first inequality for x

4*x≥3

x≥3/4

4. Set up the second inequality for the term √(,2*x−5)

2*x−5≥0

5. Solve the second inequality for x

2*x≥5

x≥5/2

6. Determine the intersection of the two solution sets. Since 5/2=2.5 and 3/4=0.75 the condition x≥2.5 is more restrictive.

x≥5/2

Final Answer

Domain=[2.5,∞)

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