Question

Find the domain and range of each of the following real valued functions : 

f(x) = |x – 1|

Answer 1

f(x) = |x – 1|

We know,

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, ∞)