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Determining whether Composition of Functions is Commutative

Avg difficulty 2.5

Using the functions provided, find f( g( x ) ) f \left(g \left(x\right)\right) and g( f( x ) ). g \left(f \left(x\right)\right) . Determine whether the composition of the functions is commutative.

f(x)=2x+1g(x)=3−x f \left(x\right) = 2 x + 1 g \left(x\right) = 3 - x

OpenStax Algebra and Trigonometry 2e, 3.4 Composition of Functions, exercise 9

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Adapted from College Algebra © 2021 Rice University. Licensed under CC BY 4.0. Sources: College Algebra 2e, Algebra and Trigonometry 2e, Precalculus 2e, College Algebra with Corequisite Support 2e. Imported at revision 4922e46.