IPMAT Indore 2021 (SA) PYQs

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

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