If f and gare continuous on [a,b] and g(x)> 0 for xE[a,b]· 1. Show that there exists cE[a,b] such that fg=f(c) | 2. Show that this conclusion fails if we do not have g(x)>0·
If f and gare continuous on [a,b] and g(x)> 0 for xE[a,b]· 1. Show that there exists cE[a,b] such that fg=f(c) | 2. Show that this conclusion fails if we do not have g(x)>0·
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.3: Factorization In F [x]
Problem 22E: Let ab in a field F. Show that x+a and x+b are relatively prime in F[x].
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