Find the Domain f(x) = square root of 25-x^2

Problem

ƒ(x)=√(,25−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.

25−x2≥0

2. Rearrange the inequality to isolate the variable term.

−x2≥−25

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

x2≤25

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

|x|≤5

5. Express the solution as a compound inequality.

−5≤x≤5

Final Answer

Domain: *[−5,5]

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