Let F(R, R) be the set of all functions from R to R. For any f, g € F(R, R), we define fog € F(R, R) by setting (fog)(a) = f(g(a)) for all a € R. (a) Prove or disprove that o is associative. (b) Prove or disprove that is commutative.
Let F(R, R) be the set of all functions from R to R. For any f, g € F(R, R), we define fog € F(R, R) by setting (fog)(a) = f(g(a)) for all a € R. (a) Prove or disprove that o is associative. (b) Prove or disprove that is commutative.
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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![Let F(R, R) be the set of all functions from R to R. For any f, g € F(R, R), we
define fog E F(R, R) by setting (fog)(a) = f(g(a)) for all a € R.
(a) Prove or disprove that o is associative.
(b) Prove or disprove that is commutative.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff2e948f6-fd6f-485f-942e-c931230f8579%2F400570f0-1e11-4819-a941-abec3fcf8a49%2Fpge8u7b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let F(R, R) be the set of all functions from R to R. For any f, g € F(R, R), we
define fog E F(R, R) by setting (fog)(a) = f(g(a)) for all a € R.
(a) Prove or disprove that o is associative.
(b) Prove or disprove that is commutative.
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