If $[x]$ represents the greatest integer function, then the set of all real values of $x$ for which $f(x)=\sqrt{\frac{[x]-x}{x-[x]}}$ is real is

If $[x]$ denotes the greatest integer $\leq x$, then the range of the real valued function $f(x)=\frac{1}{\sqrt{x-[x]}}$ is

Assertion (A) $\operatorname{coth} x=\frac{1-k}{1+k}(0 < k < 2)$.

Reason (R) The graph of $y=\tanh x$ always lies between the lines $y=-1$ and $y=1$

The correct option among the following is