Find the domain and range of each of the following real valued functions:
f(x) = |x – 1|
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, ∞)
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