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Q. Domain and range of $f(x)=\frac{|x-3|}{x-3}$ are respectively

Relations and Functions - Part 2

Solution:

The given function is $f(x)=\frac{|x-3|}{x-3}$
This function is well defined for all real numbers other than 3.
$\therefore$ Its domain is $R-\{3\}$
Now, $ f(x)=\frac{|x-3|}{x-3}$
$=\begin{cases} \frac{x-3}{x-3}: x>3 \\\frac{-(x-3)}{x-3}: x < 3 \end{cases}=\begin{cases} 1: x>3 \\-1: x < 3\end{cases}$
Range of function $f$ is $\{1,-1\}$