Domain of the function $f(x) = \frac{{{x^2} - 3x + 2}}{{{x^2} + x - 6}}$ is
$\{ x:x \in R,\;\;x \ne 3\} $
$\{ x:x \in R,\;\;x \ne 2\} $
$\{ x:x \in R\} $
$\{ x:x \in R,\;\;x \ne 2,\;x \ne - 3\} $
If $x = {\log _2}\left( {\sqrt {56 + \sqrt {56 + \sqrt {56 + .... + \infty } } } } \right)$ then
Let $N$ be the set of positive integers. For all $n \in N$, let $f_n=(n+1)^{1 / 3}-n^{1 / 3} \text { and }$ $A=\left\{n \in N: f_{n+1}<\frac{1}{3(n+1)^{2 / 3}} < f_n\right\}$ Then,
If $f(x) = \frac{x}{{x - 1}}$, then $\frac{{f(a)}}{{f(a + 1)}} = $
The period of the function $f(x) = e^{x -[x]+|cos\, \pi x|+|cos\, 2\pi x|+....+|cos\, n\pi x|}$ (where $[.]$ denotes greatest integer function); is:-
The range of the function $f(x) = \frac{{x + 2}}{{|x + 2|}}$ is