If $f(x) = x^3 - x$ and $g(x) = \sin^2 x$, then $f\left(g\left(\frac{\pi}{6}\right)\right) = $

If $f(x) = \frac{x}{2x+1}$ and $g(x) = \frac{x}{x+1}$,then $(f \circ g)(x) = $

Let $f(x) = \frac{ax + b}{cx + d}$. Then,$f \circ f(x) = x$ provided that

If $f : R \rightarrow R$ is defined by $f(x) = x^{2} - 3x + 2$,find $f(f(x))$.

Let $f: R \rightarrow R$ be the Signum Function defined as $f(x) = \begin{cases} 1, & x > 0 \\ 0, & x = 0 \\ -1, & x < 0 \end{cases}$ and $g: R \rightarrow R$ be the Greatest Integer Function given by $g(x) = [x]$,where $[x]$ is the greatest integer less than or equal to $x$. Do $fog$ and $gof$ coincide in $(0, 1]$?

If a function $f(x)$ is such that $f\left(x + \frac{1}{x}\right) = x^2 + \frac{1}{x^2}$,then $(f \circ f)(\sqrt{11}) = $