Question: Let f be a function with the property that f(0) = 1, f(0) = 1, and f(a + b) = f(a)f(b) for all real numbers

Let f be a function with the property that f(0) = 1, f(0) = 1, and f(a + b) = f(a)f(b) for all real numbers a and b. Show that f'(x) = f(x) for all and deduce that f(x) = ex.

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