Find the Domain square root of x^2-9

Problem

√(,x2−9)

Solution

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

Domain: *x2−9≥0

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

(x−3)*(x+3)≥0

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

x−3=0⇒x=3

x+3=0⇒x=−3

4. Test the intervals created by the critical points (−∞,−3] [−3,3] and [3,∞) to see where the inequality holds true.

For *x∈(−∞,−3],(−4)2−9=7≥0* (True)

For *x∈[−3,3],(0)2−9=−9≥0* (False)

For *x∈[3,∞),(4)2−9=7≥0* (True)

5. Combine the valid intervals to express the domain.

Domain: *(−∞,−3]∪[3,∞)

Final Answer

Domain of √(,x2−9)=(−∞,−3]∪[3,∞)

Want more problems? Check here!