Question

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

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

Answer 1

The correct option is A $R,[-1,1]$

$f\left(x\right)=\frac{|x-3|}{x-3}$

$x-3\ne 0$ (Denominator cannot be zero)

$\Rightarrow x\ne 3$

$\therefore$ Domain: $R-\left\{3\right\}$

$f\left(x\right)=\{\begin{array}{cc}\frac{(x-3)}{(x-3)}=1;& x>3\\ -\frac{(x-3)}{x-3}=1;& x<3\end{array}$

$\therefore f\left(x\right)=\{\begin{array}{cc}1;& x>3\\ -1;& x<3\end{array}$

$\therefore$Range $=\{-1,1\}$.