If $f(x) = \frac{3x+4}{5x-7}, x \neq \frac{7}{5}$ and $g(x) = \frac{7x+4}{5x-3}, x \neq \frac{3}{5}$,then $(g \circ f)(3) = $

If $f$ is an exponential function and $g$ is a logarithmic function,then $fog(1)$ will be

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

Let $Q$ be the set of all rational numbers in $[0,1]$ and $f:[0,1] \rightarrow [0,1]$ be defined by $f(x) = \begin{cases} x & \text{for } x \in Q \\ 1-x & \text{for } x \notin Q \end{cases}$. Then, the set $S = \{x \in [0,1] : (f \circ f)(x) = x\}$ is equal to

If $f(x) = x^2 - 1$ and $g(x) = 3x + 1$,then $(gof)(x) = $

If $f: R \rightarrow R$ and $g: R \rightarrow R$ are defined by $f(x)=x^3-x$ and $g(x)=\sin 2x$,then the values of $x \in (0, 2\pi)$ that satisfy $f(g(x)) > 0$ lie in the interval