WBJEE · Maths · Functions
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 \((-\infty, \infty)\)
- B The range is \{0\}\(\cup(-1\} \cup\{1\}\)
- C The domain is \((-\infty, 0) \cup[1, \infty)\)
- D The range is \{0\}\(\cup\{1\}\)
Answer & Solution
Correct Answer
(C) The domain is \((-\infty, 0) \cup[1, \infty)\)
Step-by-step Solution
Detailed explanation
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 \(f(x)=\{-1,0,1\}\)
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