If $x$ is real,then the range of $\frac{x^2+2x+1}{x^2+2x+7}$ is

The range of $f(x) = \frac{x^2 + 34x - 71}{x^2 + 2x - 7}$ is

The domain of the function given by $2^x+2^y=2$ is

Let $f(x) = \frac{x^2-6x+5}{x^2-5x+6}$. Match the conditions / expressions in Column $I$ with statements in Column $II$.

Column $I$	Column $II$
$(A)$ If $-1 < x < 1$,then $f(x)$ satisfies	$(p)$ $0 < f(x) < 1$
$(B)$ If $1 < x < 2$,then $f(x)$ satisfies	$(q)$ $f(x) < 0$
$(C)$ If $3 < x < 5$,then $f(x)$ satisfies	$(r)$ $f(x) > 0$
$(D)$ If $x > 5$,then $f(x)$ satisfies	$(s)$ $f(x) < 1$

If $f:[2, \infty) \rightarrow B$ defined by $f(x)=x^2-4x+5$ is a bijection, then $B$ is equal to

Let $f:(1,3) \rightarrow R$ be a function defined by $f(x)=\frac{x[x]}{1+x^{2}},$ where $[x]$ denotes the greatest integer $\leq x.$ Then the range of $f$ is