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Groups and FieldsChallengeGroups and the Group Axioms

Groups and the Group Axioms · Challenge problem

The maps f(x)=ax+bf(x)=ax+b with a≠0a\ne0 form a group under composition. For f(x)=2x+1f(x)=2x+1 and g(x)=x+3g(x)=x+3, compute (f∘g)(0)−(g∘f)(0)(f\circ g)(0)-(g\circ f)(0).