Find the Domain f(x) = square root of 16-x^2

Problem

ƒ(x)=√(,16−x2)

Solution

1. Identify the restriction for a square root function, which requires the radicand (the expression inside the root) to 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, which defines the interval where x is between the negative and positive roots.

√(,x2)≤√(,16)

|x|≤4

5. Express the solution as a compound inequality or in interval notation.

−4≤x≤4

Final Answer

Domain: *[−4,4]

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