Find $g \circ f$ and $f \circ g$,if $f(x) = 8x^3$ and $g(x) = x^{1/3}$.

If $g(x)=x^{2}+x-1$ and $(g \circ f)(x)=4 x^{2}-10 x+5,$ then $f\left(\frac{5}{4}\right)$ is equal to

For $x \in R, x \neq 0,$ let $f_0(x) = \frac{1}{1 - x}$ and $f_{n + 1}(x) = f_0(f_n(x)),$ $n = 0, 1, 2, ....$ Then the value of $f_{100}(3) + f_1\left( \frac{2}{3} \right) + f_2\left( \frac{3}{2} \right)$ is equal to

Let $R$ be the set of real numbers and the mapping $f: R \rightarrow R$ and $g: R \rightarrow R$ be defined by $f(x) = 5 - x^2$ and $g(x) = 3x - 4$, then the value of $(f \circ g)(-1)$ is

Let $S, T, U$ be three non-void sets and $f: S \rightarrow T, g: T \rightarrow U$ be functions such that $g \circ f: S \rightarrow U$ is surjective. Then,

If $f: R \rightarrow R$ is defined as $f(x) = (2020 - x^{2019})^{1 / 2019}$,$\forall x \in R$,find $(f \circ f \circ f \circ f) \left( \frac{2019}{2020} \right)$.