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  • If f(x) is an odd periodic function with period 2, then f(4) equals

If f(x) is an odd periodic function with period 2, then f(4) equals

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Solution:    Given that      f(-x)=-f(x)        .......(1)

           And                  f(x+2)=f(x)              .......(2)

            From  (2) ,     f(-2)=f(2)=f(0)      ........(3)

          From   (1),     f(-2)=f(0)=-f(0).

       Rightarrow                     2f(0)=0   Rightarrow    f(0)=0

      Rightarrow                     f(4)=f(2)=f(0)=0.

    

Posted by

Deependra Verma

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