Question

Find the domain of the real valued linear function $f$ given as below:
$f\left(x\right)=\frac{(x-1)}{(x-3)}$

Answer 1

Given, $f\left(x\right)=\frac{x-1}{x-3}$
Thus, $f\left(x\right)$ is real if $x-3\ne 0$

$⟹x\ne 3$
$\therefore$ Domain$=R-\left\{3\right\}$ $=(-\infty ,\infty )-\left\{3\right\}$.