Question

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

Answer 1

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

Step 2:Domain of function
Clearly, the function $|x-1|$ is defined for all real numbers.
Hence, Domain of function $=R$

Step 3:Range of function
Output of a Modulus function is always non-negative.
$f\left(x\right)$ will take non-negative real numbers.
$\therefore$ Range of function $[0,\infty )$.