Q72 / 180 · KCET 2021 · Mathematics

Domain of $f(x)=\frac{x}{1-|x|}$ is

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

Solution

Given function, $f(x)=\frac{x}{1-|x|}$ $\because$ Denominator can't be zero. $\begin{array}{lc} \therefore & 1-|x| \neq 0 \\ \Rightarrow & |x| \neq 1 \\ \Rightarrow & x \neq \pm 1 \end{array}$ Hence, domain is $R-\{-1,1\}$.

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

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