Question

Find the domain and range of the real valued function:

(vi) \[f\left( x \right) = \left| x - 1 \right|\] 

 

Answer 1

The given real function is f (x) = |x – 1|.
It is clear that |x – 1| is defined for all real numbers.
Hence, domain of f = R.
Also, for x ∈ R, (x – 1) assumes all real numbers.
Thus, the range of f is the set of all non-negative real numbers.
Hence, range of f = [0, ∞) .