Answers:

(i)

Square of a real number is not negative.

f (x) takes real values only when 9 – x² ≥ 0

9 ≥ x²

x² ≤ 9

x² – 9 ≤ 0

x² – 3² ≤ 0

(x + 3)(x – 3) ≤ 0

x ≥ –3 and x ≤ 3

x ∈ [–3, 3]

∴ Domain (f) = [–3, 3]

(ii)

Square root of a real number is never negative.

f (x) takes real values only when x – 2 and 3 – x are both positive and negative.

When x – 2 and 3 – x are positive

x – 2 ≥ 0

x ≥ 2

3 – x ≥ 0

x ≤ 3

x ≥ 2 and x ≤ 3

∴ x ∈ [2, 3]

When, x – 2 and 3 – x are negative

x – 2 ≤ 0

x ≤ 2

3 – x ≤ 0

x ≥ 3

x ≤ 2 and x ≥ 3

Intersection of these sets is null set.

x ∈ [2, 3] – {3}

x ∈ [2, 3]

∴ Domain (f) = [2, 3]