Q116 / 160 · WBJEE 2015 · Mathematics

For the function $f(x)=\left[\frac{1}{[x]}\right]$ where $[x]$. the greatest integer less than denotes the greater the following statemen equal to $x$, which of the are true?

  • A
    The domain is $(-\infty, \infty)$
  • Correct answer
    B
    The range is \{0\}$\cup(-1\} \cup\{1\}$
  • Correct answer
    C
    The domain is $(-\infty, 0) \cup[1, \infty)$
  • D
    The range is \{0\}$\cup\{1\}$

Solution

We have, $f(x)=\left[\frac{1}{|x|}\right]$ Domain $=R-\{f(x)=0\}$ Now, $f(x)$ will be zero, when $|x|=0$. $\Rightarrow \quad x \in[0,1)$ $\therefore$ Domain of $f(x)=R-(0,1]$ and range of $f(x)=\{-1,0,1\}$

Hence, the correct answer is options: 'B', 'C'.

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