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G Ha , Ba Pa Ma a , I c K H , Lab H a a Sa F N A caG(x) = 1 M−f(x) Clearly, g is well defined on a,b since f(x) < M for all x ∈a,b Moreover, g is continuous on a,b by Theorem 67 of M1P1 as a quotient of two continuous functions with nonvanishing denominator Now, by the definition of the supremum,M is the smallest upper bound for f This means that for any >0 the number M− is notT C g g b v> R r A C> y I X X i zColumbia( R r A) f B X g C _ 5 ^23 D0cm 327 iGator j O ̃y W Let F X B A Function For All X In R And F 0 1 Then G X F ƒgƒC ƒXƒg[ƒŠ[ ƒAƒ"ƒfƒB ‚Ì •"‰® ŠG