Question

Let $A=\{xϵR:x\ne 0,-4\le x\le 4\}$ and $f:A\to R$ be defined $f\left(x\right)=\frac{|x|}{x}$ for $xϵA$. Then A 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 C

$\left\{1\right\}$

As, $x=x,x\ge 0-x<0$
So, $f\left(x\right)=xx$
When $x<0$ i.e. $xϵ[-4,0)f\left(x\right)=x-x=-1$
and when $x>0$ i.e. $xϵ(0,4]f\left(x\right)=xx=1$ So, range (f) = 1, 1