Find the Domain f(x) = square root of 64-x^2

Problem

ƒ(x)=√(,64−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.

64−x2≥0

2. Rearrange the inequality to isolate the variable term.

−x2≥−64

3. Multiply both sides by −1 and reverse the inequality sign.

x2≤64

4. Solve the quadratic inequality by taking the square root of both sides, which defines the interval where the statement is true.

|x|≤8

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

−8≤x≤8

Final Answer

Domain: *[−8,8]

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