Let \( f(x) \) and \( g(x) \) be defined by \( f(x)=[x] \) and \( g(x)=\left\{\begin{array}{lc}0...

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Let \( f(x) \) and \( g(x) \) be defined by \( f(x)=[x] \) and \( g(x)=\left\{\begin{array}{lc}0, & x \in I \\ x^{2}, & x \in R-I\end{array}\right. \) (where [.] denotes the
\( P \) greatest integer function), then

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(A) \( \lim _{x \rightarrow 1} g(x) \) exists, but \( g \) is not continuous at \( x=1 \)
(B) \( \lim _{x \rightarrow 1} f(x) \) does not exist and \( f \) is not continuous at \( \mathrm{x}=1 \)
(C) gof is continuous for all \( x \)
(D) fog is continuous for all \( x \)
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