If $f(x) = 3x + 10$ and $g(x) = x^2 - 1$,then $(fog)^{-1}$ is equal to

Let $N$ be the set of natural numbers and two functions $f$ and $g$ be defined as $f, g : N \to N$ such that $f(n) = \begin{cases} \frac{n+1}{2} & \text{if } n \text{ is odd} \\ \frac{n}{2} & \text{if } n \text{ is even} \end{cases}$ and $g(n) = n - (-1)^n$. Then $fog$ is

If $g(x)=1+\sqrt{x}$ and $f(g(x))=3+2 \sqrt{x}+x$,then $f(f(x))$ is

If $f(x) = \frac{x}{\sqrt{1 + x^2}}$,then $(fofof)(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 $f(x) = \sin^2 x$ and the composite function $g(f(x)) = |\sin x|$,then the function $g(x)$ is equal to