Let \( f(x)=\left\{\begin{array}{ll}x-[x] ; & x \notin I \\ 1 ; & x \in I\end{array} ;\right. \)...

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Let \( f(x)=\left\{\begin{array}{ll}x-[x] ; & x \notin I \\ 1 ; & x \in I\end{array} ;\right. \) where \( I \) is the set of integers and \( [x] \) represents greatest integer \( \leq x \).
If \( g(x)=\lim _{n \rightarrow \infty} \frac{(f(x))^{2 n}-1}{(f(x))^{2 n}+1} \), then \( |g(x)|=f(x) \) is satisfied by
(a) no real \( x \)
(b) all integer values of \( x \)
(c) \( x=0 \) only
(d) \( x=1 \) only
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