Find the Domain square root of x^2-4

Problem

√(,x2−4)

Solution

1. Identify the condition for the square root function to be defined. The expression inside the square root, the radicand, must be greater than or equal to zero.

x2−4≥0

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

(x−2)*(x+2)≥0

3. Find the critical points by setting each factor to zero.

x−2=0⇒x=2

x+2=0⇒x=−2

4. Test the intervals created by the critical points: (−∞,−2] [−2,2] and [2,∞)
   For x=−3 (−3)2−4=5≥0 (True)
   For x=0 (0)2−4=−4≥0 (False)
   For x=3 (3)2−4=5≥0 (True)

5. Determine the domain based on the intervals where the inequality holds true.

(−∞,−2]∪[2,∞)

Final Answer

Domain:(−∞,−2]∪[2,∞)

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