Solve it if you can!!

Algebra Level pending

Let$$f:[0,4\Pi ]\xrightarrow { } [0,\Pi ]$$ be defined by $$f(x)=cos{ }_{ }^{ -1 }(cos\quad x)$$. The number of points $$x\in [0,4\Pi ]$$ satisfying the equation $$f(x)=\cfrac { 10-x }{ x }$$

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