6. Show that if f: R→ R is continuous and f(x) = 0 for every rational number ,then f(x)=0 for all z.7. Suppose that the function f [a, b] → R is continuous. For any natural numberk, let 21, 22,..., be point in [a, b]. Prove thta there is a point z in [a, b] such thatf(z) = f(21)+...+ f(xk)k

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Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.2: Mappings

Problem 23E: Let a and b be constant integers with a0, and let the mapping f:ZZ be defined by f(x)=ax+b. Prove...

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Show that if f: R→ R is continuous and f(x) = 0 for every rational number a, men f(x)= 0 for all z.