Numerical value of the expression $\left| {\;\frac{{3{x^3} + 1}}{{2{x^2} + 2}}\;} \right|$ for $x = - 3$ is

The domain of the function $f(x) = \frac{{{{\sin }^{ - 1}}(3 - x)}}{{\ln (|x|\; - 2)}}$ is

The function $f(x) = \;|px - q|\; + r|x|,\;x \in ( - \infty ,\;\infty )$, where $p > 0,\;q > 0,\;r > 0$ assumes its minimum value only at one point, if

Let $f : R -\{0,1\} \rightarrow R$ be a function such that $f(x)+f\left(\frac{1}{1-x}\right)=1+x$. Then $f(2)$ is equal to :

The number of functions $f :\{1,2,3,4\} \rightarrow\{ a \in Z :| a | \leq 8\}$ satisfying $f ( n )+$ $\frac{1}{ n } f ( n +1)=1, \forall n \in\{1,2,3\}$ is

Tho damnin of tho finction $\cos ^{-1}\left(\frac{2 \sin ^{-1}\left(\frac{1}{4 x^{2}-1}\right)}{\pi}\right)$ is