Let a € A and f: A → A be a function such that a ran (ƒ). Suppose that h: w → A satisfies(a) h (0) = a(b) h (n+) = f (h (n)), for all n €w.Assume that h is one-to-one and onto A. Prove that f is one-to-one. DefinitionThe set consisting of the natural numbers is denoted by w.

here we can use contradiction to prove this stetements.

Answered: Let a E A and f: A→A be a function such…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let a E A and f: A→A be a function such that a ran (f). Suppose that h: w → A satisfies (a) h (0) = a (b) h (n+) = f (h (n)), for all n €w. Assume that h is one-to-one and onto A. Prove that f is one-to-one.