9) Give the domain and range of the relation \( y=-1+\sqrt{x-2} \)

To find the domain and range of the relation y = -1 + √(x - 2), follow these steps: 1. Domain: - The square root √(x - 2) is defined only when the expression under the square root is non-negative. - Set the inside of the square root ≥ 0: x - 2 ≥ 0. - Solve for x: x ≥ 2. - Thus, the domain is [2, ∞). 2. Range: - The smallest value for y occurs when x takes its minimum value in the domain. - When x = 2, √(2 - 2) = √0 = 0, so y = -1 + 0 = -1. - As x increases beyond 2, √(x - 2) becomes positive and increases without bound, so y also increases without bound. - Thus, the range is [-1, ∞). Final Answer: Domain: [2, ∞) Range: [-1, ∞)