Find the Domain 1/( square root of x-1)

Problem

1/√(,x−1)

Solution

1. Identify the constraints for the square root function. For the expression √(,x−1) to be a real number, the radicand must be non-negative.

x−1≥0

2. Identify the constraints for the fraction. Since the square root is in the denominator, the denominator cannot be equal to zero.

√(,x−1)≠0

3. Combine the constraints. To satisfy both conditions, the radicand must be strictly greater than zero.

x−1>0

4. Solve the inequality for x by adding 1 to both sides.

x>1

5. Express the domain in interval notation. Since x must be strictly greater than 1, the interval starts at 1 with a parenthesis.

(1,∞)

Final Answer

Domain:(1,∞)

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