The domain of the real valued function $f(x)=\frac{\sqrt{|x|-x}}{\sqrt{x-[x]}}$ is

The range of the function defined by

$$ f(x)=\left\{\begin{array}{lc} 2 x-3, & \text { if } x<-1 \\ 1-x^2, & \text { if }-1 \leq x \leq 1 \text { is } \\ 3 x^2+2, & \text { if } x>1 \end{array}\right. $$

If $\sinh x=-\frac{4}{3}$, then $\sinh 2 x+\cosh 2 x=$

If the function $f: R \rightarrow R$ is defined by

$$ f(x)= \begin{cases}2 x-3, & \text { if } x<-2 \\ x^2-1, & \text { if }-2 \leq x \leq 2 \\ 3 x+2, & \text { if } x>2\end{cases} $$

then $f$ is