Question

Let $A=\{x:x\ne 0,-4\le x\le 4\}$ and $f:A\to R$ be defined by $f\left(x\right)=\frac{|x|}{x}$, then the range of $f$ is

• A. $\{-1,1\}$
• B. $\{x:0\le x\le 4\}$
• C. $\{-1\}$
• D. $\{x:-4\le x\le 0\}$

Answer 1

The correct option is A $\{-1,1\}$

We know that,
$f\left(x\right)=\frac{|x|}{x}\text{Now,}|x|=\{\begin{array}{cc}x,& x>0\\ -x,& x<0\end{array}\therefore f\left(x\right)=\{\begin{array}{cc}1,& x>0\\ -1,& x<0\end{array}$
$\therefore$ The range contains only two elements $\{-1,1\}$