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}) = $

Let $f, g :(1, \infty) \rightarrow \mathbb{R}$ be defined as $f(x) = \frac{2x+3}{5x+2}$ and $g(x) = \frac{2-3x}{1-x}$. If the range of the function $f \circ g : [2, 4] \rightarrow \mathbb{R}$ is $[\alpha, \beta]$,then $\frac{1}{\beta-\alpha}$ is equal to

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

If $f(x)$ and $g(x)$ are two real valued functions such that $f(x)=3x-2$ and $g(x)=x^2+2$,then $[(g \circ f)+(f \circ g)](x) = $

Consider functions $f$ and $g$ such that the composite function $g \circ f$ is defined and is one-one. Are $f$ and $g$ both necessarily one-one?

If $f: A \rightarrow B$ and $g: B \rightarrow C$ are functions such that $g \circ f: A \rightarrow C$ is onto,then a necessary condition is: