Scary functions(part II)!!!!!

Algebra Level pending

Let f be a real valued function, and k a fixed real constant, such that for any real x,

f(k+x)=f(k-x) and f(2k+x)=-f(2k-x)

Then,

f is even but not periodic None of these f is odd but not periodic f is odd and periodic f is neither even nor odd f is even and periodic

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