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

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

If $f\left(x^{2}+f(y)\right)=x f(x)+y$ for all non-negative integers $x$ and $y$, then the value of $[f(0)]^{2}+f(0)$ equals _________.

Let $f$ and $g$ be two functions defined by $f(x) = |x + |x||$ and $g(x) = \frac{1}{x}$ for $x \neq 0$. If $f(a) + g(f(a)) = \frac{13}{6}$ for some real $a$, then the maximum possible value of$f(g(a))$ 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?

If a function $f(a) = max (a, 0)$ then the smallest integer value of $x$ for which the equation $f(x - 3) + 2f(x + 1) = 8$ holds true is _______.