Find the domain and the range of the real function f defined by f (x) = |x – 1|.

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.