Let $f = \left\{ \left(x, \frac{x^2}{1+x^2} \right) : x \in R \right\}$ be a function from $R$ into $R$. Determine the range of $f$.

If the domain of the function $\log _e\left(\frac{6 x^2+5 x+1}{2 x-1}\right)+\cos ^{-1}\left(\frac{2 x^2-3 x+4}{3 x-5}\right)$ is $(\alpha, \beta) \cup(\gamma, \delta]$,then $18\left(\alpha^2+\beta^2+\gamma^2+\delta^2\right)$ is equal to $....$.

If the range of the function $f(x) = \frac{5-x}{x^2-3x+2}$,$x \neq 1, 2$,is $(-\infty, \alpha] \cup [\beta, \infty)$,then $\alpha^2 + \beta^2$ is equal to :

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

The domain of the real-valued function $f(x) = \sqrt{\frac{2-|x|}{3-|x|}}$ is

If $D$ is the domain and $G$ is the range of the real-valued function $f(x)=\sqrt{\frac{1-x^2}{1+x^2}}$, then $D \cap G=$