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 \( x \in \mathbb{R}\)

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if \(f\) is identically zero there is nothing to prove

Well you are proving backwards you gotta start from the beginning

i guess we have to worry about \(f\) being continuous
start by showing \(f(0)=1\)

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