If\(\;{\rm{f}}\left( {\rm{x}} \right) = \left[ {\rm{x}} \right] - \left[ {\frac{{\rm{x}}}{4}} \right]\) , x ∈ R, where [x] denotes the greatest integer function, then:

• A. f is continuous at x = 4
• B. \(\mathop {{\rm{lim}}}\limits_{{\rm{x}} \to 4 + } {\rm{f}}\left( {\rm{x}} \right){\rm{\;exists\;but\;}}\mathop {{\rm{lim}}}\limits_{{\rm{x}} \to 4 - } {\rm{f}}\left( {\rm{x}} \right)\) does not exist
• C. Both \(\mathop {{\rm{lim}}}\limits_{{\rm{x}} \to {4^ - }} {\rm{f}}\left( {\rm{x}} \right){\rm{\;and\;}}\mathop {{\rm{lim}}}\limits_{{\rm{x}} \to 4 + } {\rm{f}}\left( {\rm{x}} \right){\rm{\;}}\)exist but are not equal.
• D. \(\mathop {{\rm{lim}}}\limits_{{\rm{x}} \to 4 - } {\rm{f}}\left( {\rm{x}} \right)\;{\rm{exists\;but}}\;\mathop {{\rm{lim}}}\limits_{{\rm{x}} \to 4 + } {\rm{f}}\left( {\rm{x}} \right)\) does not exist