Find the Domain and Range g(x) = square root of x+1

Problem

g(x)=√(,x+1)

Solution

1. Identify the restriction for the domain of a square root function, which requires the radicand to be non-negative.

x+1≥0

2. Solve the inequality for x to determine the set of possible input values.

x≥−1

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

Domain: *[−1,∞)

4. Analyze the range by considering the behavior of the principal square root function, which always produces values greater than or equal to zero.

√(,x+1)≥0

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

Range: *[0,∞)

Final Answer

Domain: *[−1,∞), Range: *[0,∞)

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