Find the Domain and Range f(x) = square root of x+3

Problem

ƒ(x)=√(,x+3)

Solution

1. Identify the condition for the domain of a square root function, which requires the radicand to be greater than or equal to zero.

x+3≥0

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

x≥−3

3. Determine the domain in interval notation based on the inequality.

Domain:[−3,∞)

4. Analyze the range by considering the behavior of the principal square root function, which always produces non-negative outputs.

√(,x+3)≥0

5. Determine the range in interval notation, noting that as x increases, ƒ(x) increases toward infinity.

Range:[0,∞)

Final Answer

Domain:[−3,∞),Range:[0,∞)

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