IPMAT Indore 2022 (MCQ) 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 _______.

Let $f$ and $g$ be two functions defined by $f(x) = |x + |x||$ and $g(x) = \frac{1}{x}$ for $x \neq 0$. If $f(a) + g(f(a)) = \frac{13}{6}$ for some real $a$, then the maximum possible value of$f(g(a))$ is: