MAT 21A Lecture 9: Continuity Of Inverse And Composite Functions And IMVT
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Anotherday of continuity this time we"re reviewing inverse continuity a functionis continuous and its definedwithin an tsimply interval then its inverse is alsocontinuous thats it nofancy proof if. Continuityofcompositionsoffunctii functions obtained by composing continuous functions are yes contineuous duh fcc theorem if f is continuous at c andg is continuous at is continuous. C then the composition g of g of ex. This might all lookweird but just understand that continuous functions in a composition are continuous. Afunctionis said to have intermediatevalueproperty if whenever it takeson twovalves. italsotakenon all thevalues in between. Basically if youhave a continuousinterval every y or f c a corresponding x the graph. Look y fcx there is y orfat fig horrid fca t l l a. Ta b closedinterval oletschose arandompoint with a b and call. Noticehow point c on the xaxisthere a yo or fees on the y axis it c is. Thefunction does not take on all values between.
