Find the Domain and Range y = square root of x-3

Problem

y=√(,x−3)

Solution

1. Identify the restriction for the domain. Since the square root function is only defined for non-negative real numbers, the expression inside the radical must be greater than or equal to zero.

x−3≥0

2. Solve the inequality for x to find the domain.

x≥3

3. Determine the range by considering the behavior of the square root function. The principal square root √(,u) always produces a value greater than or equal to zero.

y≥0

4. Express the domain and range in interval notation. The domain includes all values from 3 to infinity, and the range includes all values from 0 to infinity.

Domain:[3,∞)

Range:[0,∞)

Final Answer

Domain:[3,∞),Range:[0,∞)

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