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Proving Properties of Function f(x) by ardi is a document available to read on EtoBox.

(i) The document proves several properties of a function f defined on the real numbers that satisfies two conditions: 1) the limit of f(x) as x approaches 0 is 1, and 2) f(x1 + x2) = f(x1)f(x2) for all real numbers x1 and x2. (ii) It proves that: a) f(x) must be positive for all real x, b) f(rx) = [f(x)]r if r is rational, and c) if f(1) = 1, then f is a constant function. (iii) The proofs involve using the two conditions along with induction and

Author

ardi

Language

EN