Question

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

• A. The domain is $(-\infty ,\infty )$
• B. The domain is $\left\{0\right\}\cup \{-1\}\cup \left\{1\right\}$
• C. The domain is $(-\infty ,0)\cup [1,\infty )$
• D. The domain is $\left\{0\right\}\cup \left\{1\right\}$

Answer 1

The correct option is C The domain is $(-\infty ,0)\cup [1,\infty )$

$f\left(x\right)=\left[\frac{1}{\left[x\right]}\right],\left[x\right]$ denotes gretaest integer.

Greatest integer function defined by,

$f\left(x\right)$ $=\left[x\right]$$=\{-1if-1\le x<00if0\le x<11if1\le x<2\backslash$

so the Domain of $f\left(x\right)$=$(-\infty ,0)\cup [1,\infty )$