IPMAT Indore 2022 (MCQ) PYQs

Suppose that a real-valued function $f(x)$ of real numbers satisfies $f(x + xy) = f(x) + f(xy$) for all real $x, y,$ and that $f(2020) = 1$. Compute $f(2021)$.

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

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