• swissgirl
Assume $$f: \mathbb{R} \to \mathbb{R}$$ is such that $$f(x+y)=f(x)f(y)$$ ( The class of exponential functions has this property). Prove that f having a limit at 0 implies that f has a limit at every real number and is one, or f is identically 0 for every $$x \in \mathbb{R}$$
Mathematics

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