IPMAT Indore 2024 (SA) PYQs

A set of all possible values the function $f(x)=\dfrac{x}{|x|}$, where $x \neq 0$, takes is

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

If $f\left(x^{2}+f(y)\right)=x f(x)+y$ for all non-negative integers $x$ and $y$, then the value of $[f(0)]^{2}+f(0)$ equals _________.