It is hard to compose

Calculus Level 4

\[f\left( f\left( f\left( x \right) -2{ x }^{ 3 } \right) \right) \ge f\left( f\left( 2{ x }^{ 3 }-f\left( x \right) \right) \right) \]

Let \(f\left( x \right) =2{ x }^{ 3 }-21{ x }^{ 2 }+78{ x }+24\). Find the number of natural numbers in the solution set of \(x\) satisfying the inequality above.

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