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.
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section2.7: Combining Functions
Problem 4E
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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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