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Math Help - Periodic functions

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    Senior Member pankaj's Avatar
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    Periodic functions

    If f(a-x)=f(a+x);f(b-x)=f(b+x),\forall x\in R, a>b.Then prove that the function f(x) is periodic and hence find its period.
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    Quote Originally Posted by pankaj View Post
    If f(a-x)=f(a+x);f(b-x)=f(b+x),\forall x\in R, a>b.Then prove that the function f(x) is periodic and hence find its period.
    Let x = a - t so the first gives f(t) = f(2a - t)

    Let x = b - t so the secondgives f(t) = f(2b-t)

    Equating gives

    Let f(2a-t) = f(2b-t) and setting T=2a-t first gives f(T) = f(T+2b-2a) and so the period is 2b-2a
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