Mathematics - Functions Question with Solution | TestHub

Given $f\left(x\right)=\frac{{cosec}^{-1}x}{\sqrt{\left\{x\right\}}}$

Domain of ${\mathrm{cosec}}^{-1}x$$\in (-\infty ,-1]\cup [1,\infty )$

We know, $\left\{x\right\}\ne 0,$ so $x\ne$integers. 

So, $x$ belongs to all non-integers except the interval $\left[-1,1\right].$