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) = $\begin{cases} x - 1, & \text{if } x \ge 1 \\ -(x-1), & \text{if } x < 1 \end{cases}$ ⇒ f (x) = $\begin{cases} x-1, & \text{if } x \ge 1 \\ 1 - x, & \text{if } x < 1 \end{cases}$ From above, we observe that in both cases f (x) ≥ 0. Hence, range of f (x) is [0, ∞).