Find the Domain 1/2* square root of x^2-16=4

Problem

1/2√(,x2−16)=4

Solution

1. Identify the restriction for the square root function. For the expression to be defined in the set of real numbers, the radicand (the expression inside the square root) must be greater than or equal to zero.

√(,ƒ(x))⇒ƒ(x)≥0

2. Set up the inequality using the radicand from the given equation.

x2−16≥0

3. Factor the difference of squares to find the critical points.

(x−4)*(x+4)≥0

4. Determine the intervals where the product is non-negative. The roots are x=−4 and x=4 Testing values in the intervals (−∞,−4] [−4,4] and [4,∞) shows that the inequality holds when x is less than or equal to −4 or greater than or equal to 4

x≤−4* or *x≥4

5. Express the domain in interval notation.

(−∞,−4]∪[4,∞)

Final Answer

Domain:(−∞,−4]∪[4,∞)

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