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If f(x) is periodic function satisfying the condition f(x)+f(x+2)=0 then find the period of f(x)

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Solution:   We have ,    f(x)+f(x+2)=0    

                  f(x)+f(x+2)=0       ..........(1) 

             Replace  x   by   x+2

            f(x+2)+f(x+4)=0     ...........(2) 

    From     (1)-(2)    we get 

      f(x)=f(x+4)    Hence    T=4  ( period of f(x) is 4)

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Deependra Verma

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