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 $f(2021)$.

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 _______.

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