Find the Domain and Range square root of x-1

Problem

√(,x−1)

Solution

1. Identify the restriction for the square root function. The expression inside the radical, known as the radicand, must be greater than or equal to zero for the function to be defined in the set of real numbers.

x−1≥0

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

x≥1

3. Determine the range by considering the behavior of the square root function. Since the principal square root √(,u) always produces a non-negative result, the smallest possible value occurs when the radicand is zero.

√(,1−1)=0

4. Conclude that as x increases toward infinity, the value of the function also increases toward infinity.

ƒ(x)≥0

Final Answer

Domain: *[1,∞), Range: *[0,∞)

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