$f(x) = (20 - x^4)^{1/4}$ for $0 < x < \sqrt{5}$,then $f(f(1/2))$ is equal to

If $f: R \rightarrow R$ and $g: R \rightarrow R$ are defined by $f(x)=x-[x]$ and $g(x)=[x]$ for $x \in R$,where $[x]$ is the greatest integer not exceeding $x$,then for every $x \in R, f(g(x))$ is equal to

Let $f(x) = \sin^{-1} x$ and $g(x) = \frac{x^2 - x - 2}{2x^2 - x - 6}$. If $g(2) = \lim_{x \to 2} g(x)$,then the domain of the function $f \circ g$ is .... .

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 $(0, 1]$?

Show that if $f: A \rightarrow B$ and $g: B \rightarrow C$ are one-one,then $g \circ f: A \rightarrow C$ is also one-one.

Consider the function $f: R \rightarrow R$ defined by $f(x)=\frac{2x}{\sqrt{1+9x^2}}$. If the composition of $f$,$\underbrace{(f \circ f \circ \ldots \circ f)}_{10 \text{ times }}(x) = \frac{2^{10}x}{\sqrt{1+9\alpha x^2}}$,then the value of $\sqrt{3\alpha+1}$ is equal to: