Answers:
(i)
Square of a real number is not negative.
f(x) takes real values only when x – 1 ≥ 0
x ≥ 1
∴ x ∈ [1, ∞)
Domain (f) = [1, ∞)
If x ≥ 1
x – 1 ≥ 0
√(x-1) ≥ 0 ⇒ f (x) ≥ 0
f(x) ∈ [0, ∞)
∴ Range (f) = [0, ∞)
(ii)
Square of a real number is not negative.
f (x) takes real values only when x – 3 ≥ 0
x ≥ 3
∴ x ∈ [3, ∞)
Domain (f) = [3, ∞)
If x ≥ 3,
x – 3 ≥ 0
√(x-3) ≥ 0 ⇒ f (x) ≥ 0
f(x) ∈ [0, ∞)
∴ Range (f) = [0, ∞)