Answers:

(i)

f(x) is defined for all real values of x, except when 2 – x = 0 or x = 2.

Domain (f) = R – {2}

f (x) = (x-2)/(2-x)

f (x) = -(2-x)/(2-x)

= –1

If x ≠ 2, f(x) = –1

∴ Range (f) = {–1}

(ii)

Consider,

f(x) is defined for all real numbers x.

Domain (f) = R

If x < 1,

x – 1 < 0 or 1 – x > 0.

|x – 1| > 0 ⇒ f(x) > 0

If x ≥ 1,

x – 1 ≥ 0.

|x – 1| ≥ 0 ⇒ f(x) ≥ 0

∴ f(x) ≥ 0 or f(x) ∈ [0, ∞)

Range (f) = [0, ∞)