Find the Domain square root of 16-x^2

Problem

√(,16−x2)

Solution

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

16−x2≥0

2. Rearrange the inequality to isolate the variable term.

−x2≥−16

3. Multiply both sides by −1 remembering to flip the inequality sign.

x2≤16

4. Solve the quadratic inequality by taking the square root of both sides.

|x|≤4

5. Express the solution as a compound inequality representing the interval.

−4≤x≤4

Final Answer

Domain:[−4,4]

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