So, if I understand correctly. You are trying to determine whether the inverse function of f(x) is function. First, you must find the inverse function. To do this, typically one "switches" the x and y values and solves for y. So, let's do that.

flip x and y

solve for y, first multiply both side by 3

square both sides to solve to rid of the radical

now solve for y^2

take the root to isolate y

since for any x, y (your inverse function) can have 2 values the inverse is not a function