Question

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

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

Answer 1

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

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

If $x>0$

$|x|=x$

So, $\frac{|x|}{x}=1$

If $x<0$

$\frac{|x|}{x}=\frac{-x}{x}=-1$

Range: $\{-1,1\}$