Range of the function $f(x) = 3 + 2^x + 4^x$ is

The function $f(x) = \frac{\sec^{-1}x}{\sqrt{x - [x]}}$,where $[.]$ denotes the greatest integer less than or equal to $x$,is defined for all $x$ belonging to:

If the domain of the function $f(x) = \log_e \left( \frac{2x+3}{4x^2+x-3} \right) + \cos^{-1} \left( \frac{2x-1}{x+2} \right)$ is $(\alpha, \beta]$,then the value of $5\beta - 4\alpha$ is equal to

The domain of the function $f(x) = \sqrt{\frac{4-x^2}{[x]+2}}$,where $[x]$ denotes the greatest integer not more than $x$,is

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

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	$(s)$ $f(x) < 1$