Find the Domain f(x) = square root of 9-x^2

Problem

ƒ(x)=√(,9−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.

9−x2≥0

2. Rearrange the inequality to isolate the variable term.

−x2≥−9

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

x2≤9

4. Solve the quadratic inequality by taking the square root of both sides, which involves the absolute value of x

|x|≤3

5. Rewrite the absolute value inequality as a compound inequality to define the interval.

−3≤x≤3

Final Answer

Domain: *[−3,3]

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