A set of all possible values the function $f(x)=\dfrac{x}{|x|}$, where $x \neq 0$, takes is

The function $f(x) = \dfrac{x^3 - 5x^2 - 8x}{3}$ is

If $f(1) = 1$ and $f(n) = 3n - f(n - 1)$ for all integers $n > 1$ , then the value of $f(2023)$ is

Let $A=\{1,2,3\}$ and $B=\{a, b\}$. Assuming all relations from set $A$ to set $B$ are equally likely, what is the probability that a relation from $A$ to $B$ is also a function?

The set of all possible values of $f(x)$ for which $(81)^{x}+(81)^{f(x)}=3$ is

A real-valued function $f$ satisfies the relation $f(x)f(y) = f(2xy + 3) + 3f(x + y) - 3f(y) + 6y$, for all real numbers $x$ and $y$, then the value of $f(8)$ is

Given $f(x) = x^2 + \log_3 x$ and $g(y) = 2y + f(y)$, then the value of $g(3)$ equals