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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2015

  • question_answer
    If \[f(x)\] is a periodic function and g is a non-periodic function, then

    A) fog is always periodic

    B) gof is never periodic

    C) gof is always periodic

    D) None of the above

    Correct Answer: C

    Solution :

    Let T be the period of \[f(x)\]. Then, \[f(x+T)=f(x)for\,all\,x\]                 \[\Rightarrow \]               \[gof(x+T)=g[f(x+T)]\]                 \[\Rightarrow \]               \[gof(x+T)=g(x)\] Hence, gof is a periodic with period T.


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