Numerical answer
A function f satisfies f(x+y) = f(x)·f(y) for all real x, y, and f(1) = 3. Find f(5).
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Answer: 243
Setting x=y=1 repeatedly: f(2) = f(1)² = 9, f(3) = f(2)f(1) = 27, f(4) = f(3)f(1) = 81, f(5) = f(4)f(1) = 243. In general f(n) = 3ⁿ for positive integers n (this is the functional form of an exponential f(x) = f(1)ˣ), so f(5) = 3⁵ = 243.
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