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If f(a-x)=f(a+x) " and " f(b-x)=f(b+x) f...

If `f(a-x)=f(a+x) " and " f(b-x)=f(b+x)` for all real x, where `a, b (a gt b gt 0)` are constants, then prove that `f(x)` is a periodic function.

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