Find the Domain and Range square root of x

Problem

√(,x)

Solution

1. Identify the restriction for the square root function. For the expression to result in a real number, the radicand must be non-negative.

2. Set up the inequality for the domain by requiring the value inside the square root to be greater than or equal to zero.

x≥0

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

Domain=[0,∞)

4. Analyze the output values to find the range. Since the principal square root of any non-negative number is always non-negative, the smallest value occurs at x=0

√(,0)=0

5. Determine the range in interval notation, noting that as x increases, √(,x) increases without bound.

Range=[0,∞)

Final Answer

Domain: *[0,∞), Range: *[0,∞)

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