If $f(x) = |\cos x|$ and $g(x) = [x]$,then $gof(x)$ is equal to

If $f: R \rightarrow R$ is defined by $f(x) = \frac{x}{x^{2}+1}$,find $f(f(2))$.

If $f(x) = \frac{2x+3}{3x-2}$,$x \neq \frac{2}{3}$,then the function $f \circ f$ is

If $f: A \rightarrow B$ and $g: B \rightarrow C$ are two functions such that $g \circ f: A \rightarrow C$ is a bijection,then which one of the following is always true?

Find the function $g(t)$ if $f(t)=3t-2$ and $(g \circ f)^{-1}(t)=t-2$.

Let $f(x) = \frac{\alpha x}{x+1}$,$x \neq -1$. If $f(f(x)) = x$,then the value of $\alpha$ is . . . . . . .