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A function f is defined such that for al...

A function f is defined such that for all real `x, y` (a) `f(x+y)=f(x).f(y)` (b) `f(x)=1+xg(x)` where `lim_(x->0) g(x)=1.` prove that `f;(x)=f(x)` and `f(x)=e^x`

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