Find the Domain and Range y = square root of x-4

Problem

y=√(,x−4)

Solution

1. Identify the restriction for the domain. For a square root function 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.

x−4≥0

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

x≥4

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 starts at 4 and goes to infinity, while the range starts at 0 and goes to infinity.

Domain:[4,∞)

Range:[0,∞)

Final Answer

Domain:[4,∞),Range:[0,∞)

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