Question

Domain of $f\left(x\right)=si{n}^{-1}\left(\frac{2x-\left[x\right]}{\left[x\right]}\right)$ , where $[\cdot ]$ denotes the greatest integer function, is

• A. $(-\infty ,1)-\left\{0\right\}$
• B. $[-\frac{4}{3},0)\cup \left\{0\right\}$
• C. $(-\infty ,0)\cup I^{+}$
• D. $(-\infty ,\infty )-[0,1)$

Answer 1

The correct option is C

$(-\infty ,0)\cup I^{+}$

$f\left(x\right)=si{n}^{-1}(\frac{2x}{\left[x\right]}-1)\because \left(I\right)\left[x\right]\ne 0\Rightarrow x\text{/}\epsilon [0,1)\left(II\right)-1\le \frac{2x}{\left[x\right]}-1\le 10\le \frac{2x}{\left[x\right]}\le 2;0\le 2+\frac{2\left\{x\right\}}{\left[x\right]}\le 2-1\le \frac{\left\{x\right\}}{\left[x\right]}\le 0$