Question

Find the domain and range of the real function $f$ defined by $f\left(x\right)=|x-1|$

Answer 1

The given real function is $f\left(x\right)=|x-1|$
It is clear that $|x-1|$ is defined for all real numbers
$\therefore$ Domain of $f=R$
Thus for $x\in R,|x-1|$ assumes all non-negative real numbers.
Hence the range of f is the set of all non-negative real numbers=$(0,\infty )$