If the domain of the function $f(x)=\sin ^{-1}\left(\frac{x-1}{2 x+3}\right)$ is $R-(\alpha, \beta)$ then $12 \alpha \beta$ is equal to :

If $y = f(x) = \frac{{ax + b}}{{cx – a}}$, then $x$ is equal to

Let $f(x)=\frac{x+1}{x-1}$ for all $x \neq 1$. Let $f^1(x)=f(x), f^2(x)=f(f(x))$ and generally $f^n(x)=f\left(f^{n-1}(x)\right)$ for $n>1$. Let $P=f^1(2) f^2(3) f^3(4) f^4(5)$ Which of the following is a multiple of $P$ ?

The graph of $y = f(x)$ is shown then number of solutions of the equation $f(f(x)) =2$ is

Let $A$ denote the set of all real numbers $x$ such that $x^3-[x]^3=\left(x-[x]^3\right)$, where $[x]$ is the greatest integer less than or equal to $x$. Then,