$\left\{x \in R: \frac{2 x-1}{x^3+4 x^2+3 x} \in R\right\}$ equals

Range of the function $f(x) = \frac{x^2 + x + 2}{x^2 + x + 1}; x \in R$ is

If $f: R \rightarrow R$ is defined by $f(x)=[2x]-2[x]$ for $x \in R$, where $[x]$ is the greatest integer not exceeding $x$, then the range of $f$ is:

If $f: R \rightarrow A$,defined by $f(x) = \cos x + \sqrt{3} \sin x - 1$,is an onto function,then $A =$

If $f:[2,3] \rightarrow R$ is defined by $f(x)=x^3+3x-2$,then the range of $f(x)$ is contained in the interval

The range of $f(x)=\sqrt{\frac{a-|x|}{(a+1)-|x|}}, (a>0)$ is