What is the range of the function f(x) = 2 + sqrt(x - 1)?
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Correct answer
B. [2, ∞)
Principle or equation
The square root function sqrt(x - 1) has range [0, ∞). Adding 2 shifts the range to [2, ∞).
Why this answer is correct
Since sqrt(x - 1) ≥ 0 for all x ≥ 1, f(x) = 2 + sqrt(x - 1) ≥ 2. As x increases, sqrt(x - 1) increases without bound, so the range is [2, ∞).
Example
For f(x) = 3 + sqrt(x), the range is [3, ∞).
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