Problem

Find the domain and range of the function \( f(x) = \sqrt{x - 2} \).

Answer

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Answer

The square root function \(f(x) = \sqrt{x}\) is always greater than or equal to zero. Therefore, the range of the function is \(f(x) \geq 0\).

Steps

Step 1 ：The function is defined if the expression under the square root, \(x - 2\), is greater than or equal to zero. So to find the domain, we solve the inequality \(x - 2 \geq 0\).

Step 2 ：Adding 2 to both sides of the inequality gives: \(x \geq 2\). So, the domain of the function is \(x \geq 2\).

Step 3 ：The square root function \(f(x) = \sqrt{x}\) is always greater than or equal to zero. Therefore, the range of the function is \(f(x) \geq 0\).

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