f(x) = |x – 1|

We know

Now, we have

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

Thus, domain of f = R

When x < 1, we have x – 1 < 0 or 1 – x > 0.

Hence, |x – 1| > 0 ⇒ f(x) > 0

When x ≥ 1, we have x – 1 ≥ 0.

Hence, |x – 1| ≥ 0 ⇒ f(x) ≥ 0

∴ f(x) ≥ 0 or f(x) ∈ [0, ∞)

Thus, range of f = [0, ∞)