Find the Domain square root of x^2-1

Problem

√(,x2−1)

Solution

1. Identify the restriction for a square root function, which requires the radicand (the expression inside the root) to be greater than or equal to zero.

x2−1≥0

2. Factor the quadratic expression using the difference of squares formula.

(x−1)*(x+1)≥0

3. Determine the critical points by setting each factor to zero, which gives x=1 and x=−1

x=1,x=−1

4. Test the intervals created by the critical points: (−∞,−1] [−1,1] and [1,∞)
   For x=−2 (−2)2−1=3≥0 (True)
   For x=0 (0)2−1=−1≥0 (False)
   For x=2 (2)2−1=3≥0 (True)

5. Combine the intervals where the inequality holds true to define the domain.

(−∞,−1]∪[1,∞)

Final Answer

Domain:(−∞,−1]∪[1,∞)

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