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Possible Duplicate:
continuous functions on $\mathbb R$ such that $g(x+y)=g(x)g(y)$

Let $g: \mathbf{R} \to \mathbf{R}$ be a function which is not identically zero and which satisfies the functional equation $g(x+y)=g(x)g(y)$

Suppose $a>0$, show that there exists a unique continuous function satisfying the above, such that $g(1)=a$.

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    Uhm - homework?2012-05-07
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    Patrova = [Sikhanyiso](http://math.stackexchange.com/users/30677/sikhanyiso)?2012-05-07
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    Also, almost verbatim the same question was completely answered [here](http://math.stackexchange.com/q/141293/5363).2012-05-07

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