Find the Domain square root of 1-x^2

Problem

√(,1−x^2)

Solution

1. Identify the condition for the square root function to be defined. The radicand (the expression inside the square root) must be greater than or equal to zero.

1−x^2≥0

2. Rearrange the inequality to isolate the variable term.

−x^2≥−1

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

x^2≤1

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

|x|≤1

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

−1≤x≤1

Final Answer

Domain={[x∈ℝ,−1≤x≤1]}

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