Find the Domain

Problem

√(,x−2)/√(,x+4)

Solution

1. Identify the constraints for the numerator. For the square root √(,x−2) to be defined in the real numbers, the radicand must be non-negative.

x−2≥0

2. Solve the first inequality for x

x≥2

3. Identify the constraints for the denominator. For the square root √(,x+4) to be defined, the radicand must be non-negative. Additionally, since it is in the denominator, the square root cannot equal zero.

x+4>0

4. Solve the second inequality for x

x>−4

5. Determine the intersection of the two conditions. The domain must satisfy both x≥2 and x>−4

x≥2

6. Express the domain in interval notation. The values of x start at 2 (inclusive) and go to infinity.

[2,∞)

Final Answer

Domain: *[2,∞)

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