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 $g(1)=a$.
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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