Q48 / 90 · JEE Main 2012 (07 May Online) · Mathematics

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

  • A
    $R$
  • Correct answer
    B
    $(-1,1)$
  • C
    $R-\{0\}$
  • D
    $[-1,1]$

Solution

$f(x)=\frac{x}{1+|x|}, x \in R$ 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 $=(-1,1)$.

Hence, the correct answer is option: 'B'.

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