Find the domain and range of each of the following real valued functions:
We know the square of a real number is never negative.
Clearly, f(x) takes real values only when x – 1 ≥ 0
⇒ x ≥ 1
∴ x ∈ [1, ∞)
Thus, domain of f = [1, ∞)
When x ≥ 1, we have x – 1 ≥ 0
Hence,
∴ f(x) ∈ [0, ∞)
Thus, range of f = [0, ∞)