Mathematics - Functions Question with Solution | TestHub

$f(x)=\frac{x}{1+|x|},x\in R$ If $x>0,|x|=x\Rightarrow f(x)=\frac{x}{1+x}$ which is not defined for $x=-1$ If $x<0,|x|=-x\Rightarrow f(x)=\frac{x}{1-x}$ which is not defined for $x=1$ Thus $f(x)$ defined for all values of $\mathrm{R}$ except 1 and $-1$ Hence, range $=(-1,1)$.