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Let \( f \) be a real-valued function such that,for any real \( x , f ( k + x ) = f ( k - x ) \) and \( f ( 2 k + x ) = - f ( 2 k - x ) \) for some \( k > 0 \) , Then (a) is even and periodic (c) \( f \) is odd and periodic \( f ( p - x ) = d ( x ) \) (b) \( j \) is odd but not periodic (d) \( \int \) is even but not periodic 4\( ! \)

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