Find the Domain

Problem

√(,18*x*y2)−2*y√(,2*x)=z

Solution

1. Identify the constraints for the square root functions. For the expression to be defined in the set of real numbers, the radicand (the expression inside the square root) must be greater than or equal to zero.

2. Set up the first inequality for the term √(,18*x*y2)

18*x*y2≥0

3. Analyze the first inequality. Since 18 is a positive constant and y2 is always non-negative for any real y the product 18*x*y2 is non-negative if x≥0 or if y=0

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

2*x≥0

5. Solve the second inequality by dividing both sides by 2

x≥0

6. Combine the conditions. For both square roots to be defined simultaneously, x must be non-negative. There are no restrictions on y because y2 will always be non-negative, and y itself is outside the square root in the second term.

Final Answer

Domain={(x,y)∈ℝ2:x≥0}

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