IPMAT Indore 2024 (SA) PYQs

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

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 _______.

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