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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2008

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

    A)  0                                            

    B)  2

    C)  4                                            

    D)  \[-4\]

    Correct Answer: A

    Solution :

                    Since,\[f(x)\]is odd periodic function with period 2. \[\therefore \]\[f(-x)=-f(x)\]and\[f(x+2)=f(x)\] \[\therefore \]\[f(2)=f(0)\]and\[f(-2)=f(-2+2)=f(0)\] Now, \[f(0)=f(-2)=-f(2)=-f(0)\] \[\therefore \]\[2f(0)=0\] \[\Rightarrow \]\[f(0)=0\] \[\therefore \]\[f(4)=f(2)=f(0)=0\]


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