Let F1 and F2 be fields. A function g ∈ F(F1, F2) is called an even function if g(−t) = g(t) for each t ∈ F1 and is called an odd function if g(−t) = −g(t) for each t ∈ F1. Prove that the set of all even functions in F(F1, F2) and the set of all odd functions in F(F1, F2) are subspaces of F(F1, F2).

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
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Chapter4: Vector Spaces
Section4.3: Subspaces Of Vector Spaces
Problem 49E
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Let F1 and F2 be fields. A function g ∈ F(F1, F2) is called an even function if g(−t) = g(t) for each t ∈ F1 and is called an odd function if g(−t) = −g(t) for each t ∈ F1.

Prove that the set of all even functions in F(F1, F2) and the set of all odd functions in F(F1, F2) are subspaces of F(F1, F2).

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