For a non negative whole number n, let the function fn be given by (picture). where n!= 1*2...n, with the convention that 0!=1, so that f0(x)=1, f1(x)=1+x and so on. A: Show by induction that for all non negative whole numbers n, f2n(x) is a positive number for all real numbers x. B: By using the answer from A, how can we conclude that f9: R(real numbers)-->R(real numbers) has an inverted function ? Does f10 have an inverted function? C: Given n>=0 explain that limx->0 fn(x)/ex=0

For a non negative whole number n, let the function fn be given by (picture). where n!= 1*2...n, with the convention that 0!=1, so that f0(x)=1, f1(x)=1+x and so on. A: Show by induction that for all non negative whole numbers n, f2n(x) is a positive number for all real numbers x. B: By using the answer from A, how can we conclude that f9: R(real numbers)-->R(real numbers) has an inverted function ? Does f10 have an inverted function? C: Given n>=0 explain that limx->0 fn(x)/ex=0

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.1: Postulates For The Integers (optional)

Problem 28E

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