We have f (x) = |x – 1|
Here, f (x) is a modulus function and since modulus of a real number is uniquely defined on real positive number.
∴ The domain of f (x) is R.
We see that f (x) = |x – 1|
f (x) = {

x−1	if‌x≥1
−(x−1)	if‌x<1

⇒ f (x) = {

x−1	if‌x≥1
1−x	if‌x<1

From above, we observe that in both cases f (x) ≥ 0.
Hence, range of f (x) is [0, ∞).