Let A be a non-empty set and suppose that f : A → Rand g : A →R. Define f + g : A → R by ( f +g)(x) = f(x) + g(x) Provide an example that shows sup(f +g)(A) < sup f(A) + sup g(A) holds,with f (A) and g(A) both bounded above.

we take f(x)=-1 x∈Q∩A1 x∈Qc∩A and g(x)=2 x∈Q∩A-2 x∈Qc∩A(f+g)(x)=f(x)+g(x)=1 x∈Q∩A-1…

Let A be a non-empty set and suppose that f : A → Rand g : A → R. Define f + g : A → R by ( ƒ + g)(x) = f(x)+ g(x) Provide an example that shows sup(ƒ +g)(A) < sup f(A) + sup g(A) holds, with f (A) and g(A) both bounded above.

Let A be a non-empty set and suppose that f : A → Rand g : A → R. Define f + g : A → R by ( ƒ + g)(x) = f(x)+ g(x) Provide an example that shows sup(ƒ +g)(A) < sup f(A) + sup g(A) holds, with f (A) and g(A) both bounded above.

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 be a non-empty set and suppose that f : A → Rand g : A →R. Define f + g : A → R by ( f +
g)(x) = f(x) + g(x) Provide an example that shows sup(f +g)(A) < sup f(A) + sup g(A) holds,
with f (A) and g(A) both bounded above.

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