Find the Domain and Range y = square root of x-2

Problem

y=√(,x−2)

Solution

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

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

x−2≥0

x≥2

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

4. Analyze the minimum value of the function. When x=2 y=√(,2−2)=0 As x increases, y increases without bound.

y≥0

Final Answer

Domain: *[2,∞), Range: *[0,∞)

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