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consider-f-function-Df-0-1-f-0-f-1-c-0-1-2-show-that-f-c-f-c-1-2-




Question Number 164039 by ArielVyny last updated on 13/Jan/22
consider f function Df=[0,1]  f(0)=f(1) c∈[0,(1/2)] show that f(c)=f(c+(1/2))
considerffunctionDf=[0,1]f(0)=f(1)c[0,12]showthatf(c)=f(c+12)
Answered by Ar Brandon last updated on 13/Jan/22
f(0)=f(1)  f(c+0)=f(c+1) , since f < 1-periodic  f(c)=f((c+(1/2))+(1/2))=f(c+(1/2))  Hence f(c)=f(c+(1/2))
f(0)=f(1)f(c+0)=f(c+1),sincef<1periodicf(c)=f((c+12)+12)=f(c+12)Hencef(c)=f(c+12)
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