Find the Domain and Range f(x) = square root of x-7

Problem

ƒ(x)=√(,x−7)

Solution

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

x−7≥0

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

x≥7

3. Determine the range by observing that the principal square root function √(,u) always produces values greater than or equal to zero.

ƒ(x)≥0

4. Express the domain and range in interval notation.

Domain:[7,∞)

Range:[0,∞)

Final Answer

Domain:[7,∞),Range:[0,∞)

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