Find the Domain f(x) = square root of x-2

Problem

ƒ(x)=√(,x−2)

Solution

1. Identify the restriction for a square root function. For the output to be a real number, the expression inside the radical (the radicand) must be greater than or equal to zero.

2. Set up an inequality based on the radicand.

x−2≥0

3. Solve the inequality for x by adding 2 to both sides.

x≥2

4. Express the domain in interval notation. Since x can be equal to 2 or any value greater than 2 the interval starts at 2 (inclusive) and goes to infinity.

[2,∞)

Final Answer

Domain:[2,∞)

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