Question

The range of the function $f \left(x\right)=\frac{x}{1+\left|x\right|}, x\,\in\,R,$ is

• A. $R$
• B. $(-1, 1)$
• C. R-\left\\{0\right\\}
• D. $[-1, 1]$

Answer 1

Answer: (B)

$(-1, 1)$

Answer 2

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