Let F be the set of all functions f: R S R. For f, g [ F, let f + g be defined as
Chapter 9, Problem 6(choose chapter or problem)
Let F be the set of all functions f: R S R. For f, g [ F, let f + g be defined as follows: For x [ R, ( f + g)(x) = f(x) + g(x). a. Prove that 3F, +4 is a group. b. Let a [ R. Define a function a: F S F by a( f ) = f(a). Prove that a is a homorphism from 3F, +4 to 3R, +4. c. Find the kernel K.
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