Let $f(x) = 30 - 2x - x^3$, then find the number of positive integral values of 'x' which satisfies $f(f(f(x))) > f(f(-x))$.
The first thing that I saw in the above question was that the function f(x) is decreasing for all values of x, and it's derivative is $-2 -3x^2$, which is less than 0 for all real values of x.
Now, in my opinion, this implies, that $f(f(f(x)))$ is a decreasing function, while, $f(f(-x))$ is an increasing function. Is that correct?
Also, how do I proceed from here on?