Answers:

(i)

Square of a real number is not negative.

f (x) takes real values only when x – 2 ≥ 0

x ≥ 2

∴ x ∈ [2, ∞)

∴ Domain (f) = [2, ∞)

(ii)

Square of a real number is not negative.

f (x) takes real values only when x² – 1 ≥ 0

x² – 1² ≥ 0

(x + 1) (x – 1) ≥ 0

x ≤ –1 or x ≥ 1

∴ x ∈ (–∞, –1] ∪ [1, ∞)

f (x) is also undefined when x² – 1 = 0  [denominator – 0]

x² – 1 = 0 ⇒ x = ± 1

x ∈ (–∞, –1] ∪ [1, ∞) – {–1, 1}

x ∈ (–∞, –1) ∪ (1, ∞)

∴ Domain (f) = (–∞, –1) ∪ (1, ∞)