Question

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

Answer 1

$f\left(x\right)=|x-1|$

It is clear that $|x-1|$ is defined for all real numbers.

Therefore, domain of $f=R$.

Also, for $x\in R,|x-1|$ assumes all real numbers.

Hence, the range of f is the set of all non-negative real numbers.