Find the Domain square root of 1-x

Problem

√(,1−x)

Solution

1. Identify the restriction for a square root function. For the expression to be defined in the set of real numbers, the radicand (the expression inside the square root) must be greater than or equal to zero.

2. Set up the inequality based on the radicand.

1−x≥0

3. Solve the inequality for x by subtracting 1 from both sides.

−x≥−1

4. Multiply both sides by −1 Remember that multiplying or dividing an inequality by a negative number reverses the inequality sign.

x≤1

5. Express the domain in interval notation. The values of x include all real numbers less than or equal to 1.

(−∞,1]

Final Answer

Domain:(−∞,1]

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