Question:
Find the domain and the range of the real function $f$ defined by $f(x)=|x-1|$.
Solution:
The given real function is $f(x)=|x-1|$.
It is clear that $|x-1|$ is defined for all real numbers
$\therefore$ Domain of $f=\mathbf{R}$
Also, for $x \in \mathbf{R},|x-1|$ assumes all real numbers.
Hence, the range of $f$ is the set of all non-negative real numbers.