The modulus game . . !!

Algebra Level 4

Let there be an equation

\[ f(x) =|. . . . . | | |x-2| - 2 | - 2 |. . . . | , \]

where "|. . . | " denotes modulus . Let there be 2014 times modulus in f(x) .

Find the number of roots of f(x) ?

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