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In order to challenge a broader section of the forum, there is a part a and a part b to this challenge - if you feel that part b is an appropriate challenge, then I request you do not post a solution to part a as part a is a strictly easier question than part b.
The challenge: Prove that the function f(x) = 2^{x} is not a polynomial on ℝ.
The challenge: Prove that the function f(x) = 2^{x} is not a polynomial on ℝ.