Find the Domain square root of x^2-2x-8

Problem

√(,x2−2*x−8)

Solution

1. Identify the condition for the domain of a square root function, which requires the radicand to be greater than or equal to zero.

x2−2*x−8≥0

2. Factor the quadratic expression to find the critical points where the expression equals zero.

(x−4)*(x+2)≥0

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

x=4

x=−2

4. Test the intervals created by the critical values ((−∞,−2] [−2,4] and [4,∞) to see where the inequality holds true.

For *x=−3:(−3−4)*(−3+2)=(−7)*(−1)=7≥0

For *x=0:(0−4)*(0+2)=(−4)*(2)=−8<0

For *x=5:(5−4)*(5+2)=(1)*(7)=7≥0

5. Conclude that the inequality is satisfied when x≤−2 or x≥4

Final Answer

Domain: *(−∞,−2]∪[4,∞)

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