Which of the following two-digit internal operations on the set of all real functions is not commutative? (In the explanatory prescriptions, f, g: R -> R are any real functions, and a ∈ R is any real number.) (a) Addition of functions pointwise: (f + g)(a) = f(a) + g(a). (b) Multiplication of functions pointwise: (f * g)(a) = f(a) * g(a). (c) Composition of functions: (f°g)(a) = f(g(a)). (d) Maximum of functions pointwise: (f Δg)(a) = max{f(a), g(a)}. (e) None of the above.
Which of the following two-digit internal operations on the set of all real functions is not commutative? (In the explanatory prescriptions, f, g: R -> R are any real functions, and a ∈ R is any real number.) (a) Addition of functions pointwise: (f + g)(a) = f(a) + g(a). (b) Multiplication of functions pointwise: (f * g)(a) = f(a) * g(a). (c) Composition of functions: (f°g)(a) = f(g(a)). (d) Maximum of functions pointwise: (f Δg)(a) = max{f(a), g(a)}. (e) None of the above.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.1: Postulates For The Integers (optional)
Problem 28E
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Which of the following two-digit internal operations on the set of all real functions is not commutative? (In the explanatory prescriptions, f, g: R -> R are any real functions, and a ∈ R is any real number.) (a) Addition of functions pointwise: (f + g)(a) = f(a) + g(a). (b) Multiplication of functions pointwise: (f * g)(a) = f(a) * g(a). (c) Composition of functions: (f°g)(a) = f(g(a)). (d) Maximum of functions pointwise: (f Δg)(a) = max{f(a), g(a)}. (e) None of the above.
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