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Question
Find the domain and range of the real valued function:
(iii) \[f\left( x \right) = \sqrt{x - 1}\]
Solution
Given:
Domain ( f ) : Clearly, f (x) assumes real values if x - 1 ≥ 0 ⇒ x ≥ 1 ⇒ x ∈ [1, ∞) .
Hence, domain (f) = [1, ∞)
Range of f : For x ≥ 1, we have:
x - 1 ≥ 0
Thus, f (x) takes all real values greater than zero.
Hence, range (f) = [0, ∞) .
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