Find all the strictly monotonic functions f: R→R such that f(x + f(y)) = f(x) + y, for all z, y € R. Prove that for every integer n > 1 there do not exist strictly monotonic functions f: R-R such that f(x+ f(y)) = f(x) +y”, for all z, y ER.

Find all the strictly monotonic functions f: R→R such that f(x + f(y)) = f(x) + y, for all z, y € R. Prove that for every integer n > 1 there do not exist strictly monotonic functions f: R-R such that f(x+ f(y)) = f(x) +y”, for all z, y ER.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.3: The Characteristic Of A Ring

Problem 9E: Let D be an integral domain with four elements, D=0,e,a,b, where e is the unity. a. Prove that D has...

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Question

Find all the strictly monotonic functions f: R-R such that
S(x+ f(w)) = S(x) + y,
for all z, y € R.
Prove that for every integer n > 1 there do not exist strictly
monotonic functions f : R → R such that
S(x+ f(y)) = f(z) + y".
for all 7, y E R.

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