Question

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

• A. $R,[-1,1]$
• B. $R-\{3\},\{1,-1\}$
• C. $R^{+},R$
• D. None of these

Answer 1

Answer: (B)

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, $f(x)=\frac{|x-3|}{x-3}$
$=\{\begin{array}{l}\frac{x-3}{x-3}:x>3\\ \frac{-(x-3)}{x-3}:x<3\end{array}=\{\begin{array}{l}1:x>3\\ -1:x<3\end{array}$
Range of function $f$ is $\{1,-1\}$