IPMAT Indore (SA) PYQs

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

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

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