Find the Domain square root of x^2-16

Problem

√(,x2−16)

Solution

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

x2−16≥0

2. Factor the difference of squares on the left side of the inequality.

(x−4)*(x+4)≥0

3. Determine the critical points by setting each factor to zero, which gives x=4 and x=−4

x−4=0⇒x=4

x+4=0⇒x=−4

4. Test the intervals created by the critical points ((−∞,−4] [−4,4] and [4,∞) to see where the product is non-negative.

For *x≤−4,(x−4)*(x+4)≥0

For −4<x<4,(x−4)*(x+4)<0

For *x≥4,(x−4)*(x+4)≥0

5. Combine the intervals that satisfy the inequality to express the domain.

(−∞,−4]∪[4,∞)

Final Answer

Domain:(−∞,−4]∪[4,∞)

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